I have the same problem with my HTC 8X. First, my original device would randomly power cycle throughtout the day (minor annoyance really, but why live with it). Searched forums, saw that was a known issue, Verizon sent me a replacement device within 24 hours. Now that it is not power cycling randomly, I noticed the cellular connection dropping out. I installed the "Hardware Tests" application and when I notice that I can't open apps such as ESPN or IE, look at the Test App and see that Network is available with signal, but Network Connection = off. A power cycle solves the problem and the device I suppose gets "refreshed" by teh network and back to normal. Tech support from Verizon said "you should power cycle your phone every day". This does not sound like a legitimate fix.
WHY IS THE CONNECTION DROPPING OUT? Why does the device suddenly "forget" the network protocol and only "remember" it when power cycled? HTC and/or Verizon need to do somehting to fix this.