I'm having similar issues with mine, somewhat indicative of a storage system fault. It'll hang at a black screen when trying to open (or switch to) an app, just showing the clock in the corner, for about 10-15 seconds, then show "Resuming" or "Loading" for another 15 or so seconds, and eventually fall back to the previous (app or launcher) page as if I backed out of the app. About a minute later, the phone will reboot on its own no matter what state the phone's in. Seems like maybe the internal storage goes offline, akin to a desktop computer getting its SATA or IDE cable pulled from the hard drive, and the system just slowly comes to grips with the fact that it can't read data anymore, then reboots.
Starting to think it's a hardware problem, like the lazy manufacturing flaws that led to the past (and even ongoing) problems with nVidia and AMD chipsets. Weak solder joint producing intermittent problems, maybe. Took mine to T-Mobile and they had a warranty replacement set up without even giving me a chance to show the problem in action.
It's still a $150 phone, and I'd say this fits within the realm of reasonable failures given the price.