Sorry to hear you're having this problem. I'd be happy to try and help.
Unfortunately I haven't been able to reproduce the problem on my test servers (I've attempted editing active menus while FeedWordPress was running, and didn't see any disappearances or other problems with the menus.) Could you let me know a bit more about (1) which version of FWP you're using, (2) which version of WordPress you're using it with, (3) which menus you're having trouble with, and (4) the specific circumstances or tests that led you to conclude the problem is linked to FWP? This information should help me get a better grip on how to troubleshoot the problem.