I'm a big fan of the Desire, but I can't help thinking that I'm constantly searching for apps to make the phone work how I would like it. The standard music player, email, sms, and browser are all a bit rubbish.
Luckily Handcent takes care of sms and Dolphin HD takes care of browser, but I haven't found a really good music player yet (there are plenty that are ok).
The Desire is a really good phone and if the developers keep adding new and better apps then it will be a great phone, but it's a long way off I reckon.
Which is why I was quite pleased when 3 offered me an iphone 4 on upgrade. I look forward to being regarded as a retarded sheep.
In answer to the OP it does sound like it's a task killer app that's force closing the music players. Check the settings.