Sharing my experience:
I picked up my phone first thing this morning....it started rebooting when I got home. I thought it was just going through updates since it was new, but I realized that it was randomly rebooting. My signal at the house isn't very good, so I too think it has to have something to do with signal strength. Took it back to the store, where I had full signal, and it never rebooted. I'm going out of town for a few days, and will see if a solution has been offered when I return.
Activated Wed afternoon I live in an area with weak service but seemed to work okay. Left home for first time with phone this afternoon and went through some areas of not so good service. Thought rebooting was related to live wallpaper....not. Then thought it was WeatherBug as it was frozen. Removed WeatherBug. Thought I had it. Then rebotted again. Probably happened 20 times since 5 pm. I was getting ready to put my old Blackberry 8830 on ebay. May have to hold off. Please give us a phone that works already.