Chiming in...
I have an iPhone 4S, MD239PA model, came with iOS 5.0.1 (9A406) out of the box, and the first 3 weeks was fine, suddenly the phone heats up while using a SIM with Alternate Line Service feature (swapped with other non-ALS SIM, and didn't heat up). Update to iOS 5.1, and after 2 weeks, the phone having "No Service" issue, or shows "Searching..." status for some time (and eventually "No Service") while on good coverage (old phone shows 4 out of 5 signal bar).
2 days ago, succesfully got signal, quite happy that it can reach network, but I was so impatient, so that I tried turning on Airplane mode, and turn it off again, then no more luck -- "No Service" again.
Tried out all suggestion around the web, but none really fix the problem.
Haven't tried to change the SIM to 64K or 128K though. I'm a traveller, and I would like to be independent for using any kind of SIM card.
I had ipad2 running with any SIM Card you like, and had no problem with batteries nor signal.
I wish the baseband or any setting used for this ipad2 can be transferred to my iPhone 4S.