It's a widely known issue (lots of posts on 'net about it - I've had it for ages) - some machines, it just will not install correctly. You can go through all sorts of 'fixes' (there are plenty of them) on the net, and they can work for the session you have it open. BUt on restart - back to same issue. It's one of the reasons why I switched to FF3.
There is a beta of flash10 http://labs.adobe.com/technologies/flashplayer10 that seems better, but I've not had much play-time with it to see if it's a complete cure
Maybe I'm wrong, but this just goes to support my suspicion that there is no one media player that works on everyone's computer. Providing a choice is the answer.
Until computing is "standardized" like television (and it really isn't, i.e., PAL, NTSC, SECAM) this challenge will persist.