Well, the good news is LiveType is apparently fine; it's fixing the problem.
You say nothing about how often you "clean up" your system and it can make a difference. Quirky behavior (and that's what it looks like from here) could be a result not restarting routinely, not repairing permissions, etc.
If your system is spic and span, it's possible that FCP's underlying project database is breaking up. This can cause some very odd behavior. Try copying your timeline into a new project and see if the re-linking is required. If your project is large and complex, break it up into multiple sequences. Using nesting can prevent issues with inadvertently altering composited items.
If your "Layered Photoshop files" are PSDs because you need transparancy, consider using PNG files instead.
There are a few places where PSDs are actually needed, but there are also a lot of things to go wrong.
hope this helps