I have the same problem on my 4g iPod Touch. Make that the first one and the replacement Touch.
As soon as I brought home my new Touch the preinstalled Apple apps would suddenly shut down. I talked to tech support and tried everything they suggested, including restore as new iPod, hold down both buttons, etc. Nothing worked so I made an appointment with the Genius Bar, and they gave me a new Touch. Tried it out at the store and it worked fine Came home, synced with desktop, downloaded lots of apps, suddenly apps closed unexpectedly, so figured it was related to my wireless setup, even though my iPhone and iPad had no problems.
Restored Touch as new iPod, using my laptop this time. Set everything to sync manually through iTunes, not wirelessly. Downloaded no music, no nothing Used only the preinstalled Apple apps for a few days. All good. Downloaded Audible and listened to books. All good for a couple of weeks.
Today, back to the old problem. All apps shut down, including Settings and Safari. Plugged into laptop, restored, once from Touch backup, once as new iPod. Still a problem.
Only thing that has changed is that our AT&T U-Verse (TV, Wireless, and phone) has been screwed up and they came out last night and worked for several hours. System down during that time. Technician said I now had a new wireless network, but it seems I have the old network and a new one, too. Although the Touch crashed this morning using the old network, I changed it to the new network. Same problem.
I reiterate that all this time, since buying the new Touch, I have never had a problem with my IPad 2 or iPhone 4S.
So, is my Touch not playing nice with my wireless network, or is it something else?