Hi,
I have the same problem with an iPhone 4 16GB Factory Unlocked. I tried 2 SIM Cards, restored it multiple times, reset network settings, turned phone on and off, airplane mode on and off, upgraded from iOS 4 to 5.0.1, and still have the same problem. The most it kept the signal was up to 9 hours, than it started repeating the problem.
Sometimes the phone drops signal to one bar and comes back up to full signal; which does not really bother me, since its only about 5 seconds without signal. But the main problem is, when the phone is idle, on the table or pocket (so it is not the case of covering the anntena with hand), it drops the signal and it shows Searching for some seconds and then it says No Service. Sometimes the Airplane Mode On Off works or Turning Phone On and Off. Additionally, the problem also occurs with using the phone with other apps.
I don't have an Apple Store in my country, and the local phone repairs said that we can't do anything. One phone repair shop said it must be a hardware problem, and that he can TRY to fix it (the part try was a little risky for me).
Phone was never dropped to ground or anything of that nature. The reception of signal from local carriers is very strong all around the city.
Any help is really appreciated.