Shipyards, like basically all installations, require people to work them. If you run out of workers at a colony, all things that need labor get reduced efficiency. If you had so many shipyards that the manpower requirement was 10x what was actually available, that would lead to work progressing at 1/10th speed.
On the colony summary screen it shows how many workers are needed for all installations, broken down by type. And at the bottom is a sum showing if you have excess or insufficient workers.
If you have insufficient workers, the "Economic efficiency modifier" in the second column will show the effects by being less than 100%. A few other things can ALSO cause that to drop (running out of wealth, radiation), but a labor shortage is a very common one.
