I had a similar issue on one of my A-1s. With the bottom cover removed, I took a slow motion vid of the function of the camera and was able to spot the issue. There are 3 magnets in the AE-1 and A-1, and I assume the AT-1 would be similar. The two magnets that control the shutter screens are visible with the bottom plate removed. The third is for aperature and it most likely not related to this issue. The opening shutter magnet is usually protected by a plastic cover. This is a twin magnet in that it has a standard magnet as well as an electro-magnet. It does not sound like that is the issue here. The other magnet is an electro-magnet only and that one controls the release of the closing curtain. Take a close look at how that one is working.
From the sound of the issue, that could be dirty and sticking or, the trigger that causes the signal to the magnet to stop might be at fault. If it is just sticking, you might be able to clean the magnet to restore reliable function. I have not fixed this type issue before since in my case, the magnet itself was bad and needed replaced. The magnet armature wire on the magnet is extremely fine and could be damaged very easily. Don't try to clean the magnet with a brush as that could easily break that tiny, thin wire.
Hopefully, this was helpful.