I think I would keep an eye out for a different, good condition FE and have it overhauled rather than putting more money into the one you have. It is unusual to have recurring problems with these cameras, you maybe just have one of the few bad ones. If I really liked shooting with it, I wouldn't let one bad one discourage me completely.
Originally Posted by Dr.Pain-MD
In general, not to Dr. Pain since he did get his FE serviced:
I have accumulated a lot of these from the FM/FE family as well as an F2 and F3. I have spent the money for a professional overhaul for all of them, I just include that in my expected expenditure when I buy one. I wouldn't expect a 30 year old car to run at it's prime without having spent money for oil changes and tune-ups, why should I expect my camera to just work indefinitely? I have a EX condition FG coming from KEH right now. If I really like it and decide to keep it, It will also get an overhaul. I've had very good luck with KEH repair (more expensive) and Garry's Camera Repair (much less expensive). Great turn-around and good quality of work from both.