I haven't used the Sprint TV app on my Evo, as yet. But if it's anything like Sprint TV on my old PalmOS Treo, or my Palm Pre, it is designed to stop playing when it is off screen. It is first and foremost, a video-focused application. If you don't have it showing onscreen, you're not watching your "TV program", so to save power and bandwidth, it stops playing. Voila...
HTH,
-Jerry
PS/BTW/FWIW - Of all the music apps I've tried over the last couple of weeks, I like Mixzing the best. Cherry Rplayer is a nice streaming radio app, and I'll be trying others.