I seem to remember a like problem I had many years ago with my FE2.

New batteries fixed the problem.

You could check out the shutter changing by listening to the shutter when you set it to the manual 1/250 setting, (red on the dial). The run it through some of the lower speeds.

I would though try the battery first, my FE2 does go through a few and especially if they have sat in the body for a while then get used.