The intermittent nature of the problem definitely indicates a server-side issue. Maybe there is a connection pool issue--some crusty old code not disposing of connections appropriately, perhaps? Could be disk usage is being thrashed...though it seems that wouldn't be likely to give an immediate error response unless the problem has been bad for a long time.
In the past few weeks or so, I've noticed that the connection to the forums seems slow and/or unstable. I am often seeing the "SMF not available" page, which usually appears when the forum is actually down, but in this case I can often get back to the forum by refreshing the page a few times. It comes up seemingly randomly.
I am curious if this is affecting others, if this is a known issue, and/or if the problem is on my end and there are some steps I can take to fix this. N.B., I am seeing the same behavior on multiple devices that I use to browse these fine forums, so I doubt it is due to a device-specific issue in this case.