I don't personally know anything about FLcomp itself, however, to make it easier for those who to do help you, here's a few things you could do:
Try running it as admin
Uninstall, and download a fresh copy of the files, not just updating.
Also, when reporting errors, its best to expand the arrow that says "view problem details". A screenshot including that would be far more help to people who know about it than just a 'stopped working' dialogue box. I don't personally know if FLcomp has an error log, but I imagine it does, and that's probably got a line or two that would be useful to someone in-the-know.
To reiterate: 'stopped working' dialogues gives no information about why, and so no-one can help you aside from the basic troubleshooting.
EDIT: Personally using 2.02, not had a single issue, so while downgrading may cure the symptom, I doubt it's a program issue. Probably compatibility or somesuch.
EDIT2: Not sure how LFcomp works, but some programs run their auto-update check on startup, and if it cannot connect, might be hanging and not initialising the actual program. This would probably a firewall issue. Howwwwwwever, it's unlikely, 'cos... well, that's a stupid mistake for a programmer to make. I'm just saying, I did that, but I think Wizou's smarter than me...