I guess misery loves company, because I've had the same issue. It's really bad. It started with Pandora. I thought, hmmm...maybe it's the app, so I moved over to Slacker. Same thing. I tried Google Music, but had the same issue. Without fail, my DX reboots within a minute or two. I've also noticed that the 3G connection will disappear completely, and I have to reboot to get that back, too.
I has to be something with the way Motorola codes the OS because when I was rooted on Froyo, I didn't have any reboot issues. When I removed root, the random reboots started up almost immediately.