Edit: After deleting all shipyards and just creating a single yard for each class the build time is now as follows:
Amon: 1 slipway = 38 months, 36 slipways = 47 months.
Amonx6: 1 slipway = 64 months, 6 slipways = 47.5 months.
Amonx36 1 slipway = 68 months

Edit: Once you reach 127,000 naval tons total build rate starts going down across every shipyard.
You lose about 10% build rate for every increase of 127,000 tons of naval, and approxximately 1,270,000 commercial.

You...
I'm pretty sure this is not a bug. Most likely cause in this situation: You do not have enough workers to man the shipyards.

From Part 3, Section I:The 10-year holiday (later extended 5 years by the London Naval Treaty) is mentioned in every work on the subject I've ever read. 

Bha, one should not check sources late at night. I specificity remembered (and checked) that states built ships in the period but missed that those were covered in the treaty as exceptions. Still only applies to capital ships though (yes those others were covered as well in the London treaty some 8 years later).

Reliable sources on this say differently.  The British fleet had been worked very hard during the war.  The USN was in slightly better shape, but there was a reason why almost all of the retained battleships had their machinery replaced.  It was just not possible at the time to make a machinery plant that would last more than 15-20 years.  And real-world refits don't work like they do in Aurora

Thus the imo. And of course ships and material age. That said, you dont go out and buy a new car just because the radiator is broke. Now yes, there is a bit of a difference between ripping out the boilers of a bb and changing the radiator, but as long as the overall design is not obsolete (as one could argue that for example the Dreadnought class was) it is still far cheaper then building a whole new ship.

It said nothing about building new battle ships (and note that I separate battle ship from battleships). The WNT only limited how many/big/armed and total displacement of capital ships you could have. You were completely free to build new ones if you wanted as long as you removed the old ones. Also the WNT said nothing (apart from individual size of the ship) about battle ships that were not capital ships. The London NT 1 and 2 later placed restrictions on cruisers, destroyers and submarines as well and those restrictions were similar to the ones above (aka size, armament and total displacement of the fleet). Nowhere does it say anything about not building new ships...........................

From Part 3, Section I:

(a) Capital ships and aircraft carriers twenty years after the date of their completion may, except as otherwise provided in Article VIII and in the tables in Section II of this Part, be replaced by new construction, but within the limits prescribed in Article IV and Article VII. The keels of such new construction may, except as otherwise provided in Article VIII and in the tables in Section II of this Part, be laid down not earlier than seventeen years from the date of completion of the tonnage to be replaced, provided, however, that no capital ship tonnage, with the exception of the ships referred to in the third paragraph of Article II, and the replacement tonnage specifically mentioned in Section II of this Part, shall be laid down until ten years from November 12, 1921.

The 10-year holiday (later extended 5 years by the London Naval Treaty) is mentioned in every work on the subject I've ever read. 

And I am of the opinion that most of the warships that got decommissioned (and sold for scrap) after ww1 was so because states needed money in a really bad way, not because they were worn out. Obsolete I might agree on, depending on what ship we are talking about, but not worn out. I mean, lets take Dreadnought herself as an example. Commissioned in 1906, decommissioned 1919. During this time she was refit (at least) twice (and do note that this was before the treaty), the last time started just before the end of the war (and just before being decommissioned) when, imo, the UK government realised they needed cash badly and sold here for scrap. I have a hard time believing that she was "worn out" by that time.

Reliable sources on this say differently.  The British fleet had been worked very hard during the war.  The USN was in slightly better shape, but there was a reason why almost all of the retained battleships had their machinery replaced.  It was just not possible at the time to make a machinery plant that would last more than 15-20 years.  And real-world refits don't work like they do in Aurora.  No matter how often you refit, ships still age.

Fun fact, she is the only battleship to take out a submarine and she did it by ramming

Yes, I was aware of that.  I am also aware of the Bunga Bunga plot where a bunch of fake "Abyssinians" got aboard.

As far as I know that treaty came about because it was bloody expensive to build new ships.

That, and the popular perception that the naval arms race contributed to the start of WWI.  Nobody wanted to have a building race, which seemed to be forming before the WNT was signed.

And the treaty did not say that you could not build new ships, only how many and how big.

Uhh....
It did say you couldn't build new battleships.  Thus, if you wanted better battleships, you had to make them out of your old ones.  Nobody did big refits on other types of ships, because there was no point in doing so.  It was better to throw the old ones away and build new ones. 

Now this had a couple of things to do with the arms race that was going on at the time that none really wanted to pay for, but that was more of navies expanding rather then replacing. And you dont really build a big bb just to throw it away a couple of years later, they are way to expensive for that.

Not really.  The service life of a warship was a lot shorter back then.  The early dreadnoughts were worn out by the end of the war, and they were maybe 15 years old.  They'd have been headed into reserve anyway, if the treaty hadn't sent them to the scrapyard instead.  For another example, take the flush-deckers.  The ones that survived into WWII were about 20 years old, and had pretty much all spent significant time in reserve.  The ones that didn't spend time in reserve had been scrapped because they were worn out.  It's often cheaper in the long run to build a new ship than to upgrade an existing one (something politicians today have trouble understanding), but it was the way of things back then.  Also, design art was evolving a lot faster back then than it is today, which meant that ships became functionally obsolete much more quickly.

The same was done to some of the USN battleships during the 20s.  However, that armor was non-structural, and doing so was very expensive.  Which is why it wasn't done more.  They were rebuilding ships because they weren't allowed to build new ones, not because it was the best solution overall.

This is very correct.   Under the Naval accords they could not build new ships, so they rebuilt old ones.  If they could build and replace they would of built and replace.

Due to the increased flexibility of smaller ships, other then the RP or sheer giggles of having a deathstar floating around to devastate worlds, you are generally better off IMO (Which is not that great in this game) to have a fleet of smaller ships, as if anything, you are not tethered to one yard for building and maintenance.   Also, if you can build 2 big ships, or 20 smaller ships, and in combat by missles or mesons you have 10% damage.  In the 20 ship fleet you will have more then one spot to do repairs, even if you lost your fleet ships they will be quicker to be replaced and still have 90% of your fleet in operation.   If one of your big ships gets damaged, you have to deal with it by shipping it far away, and while it being repaired for 10% damage (assuming you have a yard big enough open to fix it) you have 50% of your fleet not in operation.   

Also putting too many eggs in a few ships means that if you have issues in more then one spot your super-deathstar can't be there in one time and you can lose hole systems, while a smaller ship navy can at least hold the line till reinforcements come.

It takes about 25 years to expand a yard large enough for that ship, and 48,000 neutronium and duranium to upgrade it.
The yard itself requires 41 million people to run too.
Of course a yard with smaller slipways but equal total tonnage costs exactly the same to build and run, but ships built from that will be made slightly faster.

@Rich.h. Modern militaries commonly employ major designs, which go through modifications over its service life, and eventually are supplanted by a future, vastly different design. This suggestion is natural extension of Aurora upgrade system that tries to take that in to account. Our upgrade system include three elements:

• The first are the "basic/core" components which has no upgrades or will upgrade immediately when the background tech is researched, with no cost, and no requirement to go to port. I imagine those as things can be handled by the crew like software updates or things made available with basic maintenance supplies. (unchanged)
• The second are "design" components these need to be designed, prototyped and installed when the ship is in port. Limited internal system upgrades can affected in the original slipway, cost considerably less than building a new ship, but take more time. I imagine those as modular compartments replacement install a higher res radar, outfit a turret, etc (unchanged)
• The last is hull armor retrofit which is a fundamental change to the ship structure, not a paint job. These should be a substantial undertaking that cost resources based on the size of the project.(changed)

Right now with miniaturization, ever expanding shipyard capacity, and no diminishing returns to building bigger (Which I suspect that NPR generation don't take into account) its a system with only upsides that doesn't encourage verity. Also you can keep retrofitting the same ship from "wood" to super duper technobuble tech over the course of centuries.

This suggestion offer the same, but offer more options by making smaller ship more economically viable long term.  Its realistic, its great from RP stand point (older capitals with newer escorts), and most of all for you its non-intrusive i.e. Since hull armor retrofit aren't that common, this sort of ship upgrade system would have a single design live for quite a long time; Unlike overhauls, it requires no endless micromanagement; and it offers no hard limits, only little thinking and planing. So your emperor can still build his megalomaniac projects and upgrade, at a cost.

p.s. Sorry had no time to read all the post since, or make more than this quick reply. Hopefully I didn't miss anything.

Edited.
Btw, people please don't forget its not about the economical constraints of big fleets, but whether a person with the same industrial capacity is better investing resources in either building 400kt shipyards\ships or twice as many 200kt shipyards\ships, for example.