Hard reset and the sim solutions are all possible solutions and they are also solutions you can try out yourself for the moment. Apart from them, you other option is the care point . There is nothing else you can do yourself without invalidating your warranty and you don't really want to do that if at all possible.
to clarify the issue, the problem is absolutely not seen when the phone is forced is Edge.
a problem with 3G signal then?
that's a work around, even though it is a shame to use such low speed internet in 2012...
I have the same problem and Nokia agent in my country told me that i must change the phone's board.. it is really shame on nokia that the 7.8 offcial update for my lumia 800 broke my mobile!
PROBLEM SOLVED !!!
I updated to the latest version available 2 weeks ago, and since then... not a single reboot !
I believe that if you force an update (you can find tutorials about it on the web: use zune for windows, check for update, and disconnect your pc wifi connection at the right time...) that would solve the issue (just like a repair, in the end)
I think that this update was the perfect solution, as I kept ALL MY PERSONNAL DATA (a RESET or device change as not a solution)
The best thing to do is to restore factory settings of your phone and then update software.
my lumia 800 had a similar issue till i did this.
To restore factory settings: switch off the phone then hold down down volume button, power button and camera button, when phone vibrates release the power button but hold down the other 2 for anothe 10 seconds then the phone will restart with factory setting.
NOTE: YOU WILL LOSE ALL DATA, SO BACK UP.
ALL THE BEST!