Had this problem also, IP4 kept "dying". We had restored from IP3G. AT&T manager told us what to do - we deleted all the backup (ipsw) files in itunes, plugged in the ip4 and went through the whole process again but this time chose "set up as new iphone" and after that finished, sync'd the phone a couple more times to get back the music, photos, etc. So far so good, the iphone 4 hasn't frozen up or "died" at all, so apparently it was a problem with using the old 3G backup file to restore from (and we had NOT updated to ios4 on that 3G). Hope this helps someone, it was really frustrating and nearest Apple store was 1-1/2 hours away.