I have exactly the same problem. I'm using EE in the UK. What is your network provider? They already exchanged my phone so it is most likely not connected to a single device. It must be either a software issue with the iPhone (most likely) or alternatively an issue with the sim card (I'll have that exchanged later this week).
Here are more people with that issue:
Well glad I'm not the only one.
I'm on three network and it was great on my iPhone 4 always picked a signal up.
Now then after hours of reading I tried the soft reset on my iPhone 5 and it's not completely
Solved the problem but it does seem to pick the network back up after a few mins ( a lot longer than on my Ip4 ).
I hope apple sort this out soon as its looking it is a software problem.
When an iPhone (or any cell phone) loses signal it tries to reacquire it immediately. If it fails it waits a few sconds and tries again. If it again fails it waits longer and longer between tries, because each try drains a fair amount from the battery. It can eventually get to a minute or longer between tries. BTW, you can be within the range of a tower and still lose signal because all the channels are in use.
There's nothing to fix; this is the way it is designed to work. You can force it to do a rescan by turning it to Airplane mode for about 30 seconds. As the three network is the sparsest in the UK it is not unlikely that you can lose signal for long periods of time.
My iPhone 5 does this. I got a similar answer to the one given by Lawrence Finch from an Apple genius. Thing is, this has never been an issue for me with iPhone 4, or 3G. And it's not only a minute or so, it seems to give up completely. My phone now regularly sits for an hour with no signal before I notice it and flick the flight mode. I've missed important calls and text messages. I can't accept this is a good explanation. Fair enough, I understand the principle but primarily this is a phone, not a battery saving device. It should not stop looking for service until you manually intervene surely?
Try turning off LTE in Settings. I've seen reports that LTE has difficulty reacquiring signal sometimes. This is a workaround, not a solution, but it may help until a real fix is released.
BTW, I had similar problems with Verizon's LTE with a wireless hotspot a couple of years ago, when their network was new. The problem there was once it was connected to LTE it would not switch back to EVDO if it lost the LTE signal.