Try the iPhones and if that fails, find a friend who has a Samsung and CPR on it. Preferably at your friend's place. It is not impossble that the cell tower where you are is too busy or for some other reason rejects connection attempts.
EDIT: A couple of weeks ago I was actually having the same problem - as the phone was working all right, it'd lose signal and wouldn't be able to reconnect. Even if I would successfully CPR on the 904SH, when I put the SIM + hypersim back in the 005SH, there'd still be no signal. I also tried to CPR only the SIM on an ancient Samsung - it would work there but as soon as I re-attached the hyperim (tried three different) - no signal. Eventually, the SIM (only) would no longer work on the Samsung.
So I went and asked for a
SIM replacement (costs 7 USD here because I had to report it as "stolen/lost" - they wouldn't accept it as "defective" because of all the cutting and thinning down I'd done

). And it worked right away! I guess at some point the SIM gets "damaged" or something and will no longer work with the hypersim. So, my advice is, go and get yourself a new SIM card. First have it activated (call it) on the iPhone - let's assume that Nokias aren't much good for CPR purposes - and then attach the hypersim and try it on the 007SH.
EDIT: Have you checked if the 007SH actually detects the presence of a SIM inside (although the Nokia does detect it)? You can do this by enabling PIN input. If the phone doesn't ask you to input the PIN, then it is a SIM issue which should be solved by getting a replacement.
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