A fix that worked for me! Read on.
My Iphone 4 had this problem about a month ago (full strength, searching, no signal, full strength every 30 seconds or so) on AT&T in the US. The searching seemed to crush battery life. I took the phone to Genius bar and they replaced the phone - pretty much no questions asked. They then said, if I still had the problem to go to AT&T and have them swap the sim. They also told me when I got home to set it up as a new iphone (it was still 4.x), upgrade to ios5, then restore my backup - which I did. All was fine, seemed the problem was sorted. And it was fine - for about 2 weeks.
Two weeks ago it started again on the brand new phone. Tried all sorts of resets and restores,to no avail. Finally I set it up as a "new iphone" again. And the problem went away. I manually copied all my files, apps, media, etc (good opportunity to clean up I reckoned). And it was fine.
Yesterday it started again. Yes, turning off cellular data did make it stop cycling, but was simply not an option for my business usage. A trip to the AT&T store today swapped the sim - in fact 2 sims - and no fix. Sitting in AT&T it was cycling right there in front of them. AT&T assured me they had no other types/brands of sim (64/128, etc) and that even though Apple had already swapped the hardware, it must still be an Apple hardware problem.
Out of desperation, without time to head to the Genius bar, and not being near a PC to connect to restore completely, I tried the "Reset network settings". No Luck. Then I noticed "Reset ALL settings". I figured what the ****, I'll reenter my email info, etc so I chose it. It asked me if I wanted to set it up as a new iphone (I said yes) -rebooted itself, asked for a pin again, went through the intro "welcome to iPhone" stuff after reboot. When asked I left location services off just to simplify things - and it worked!! Better still, it had all my settings still intact which I didn't expect (it said it would leave media).
So... it's been fine for several hours... battery seems ok too. If you're having this problem, try
- swapping sim if possible
- resetting all settings
- leave location services off during initial dialogs.
Worked for me.. for the time being.
Apple- this problem really exists!!!!