Same problem here and after I read through all comments it can certainly not be an issue of the network operator(s). Since, everyone uses different operators and the issues occurs in many different countries and occured for the first time already in 2012. (You would expect it is solved by now!)
I have my iPhone 5s only 1 week and the problem has occured now. The hint with resetting the network settings has worked for me (at least for the moment...). However, this is still not a solution for the problem in general. I miss customer support and an initiative from Apple here!!!
on 8/13 my iphone 5s died from not being charged when I was able to get it charged it had "no service" at the top. when I do get any signal it is 1 bar and says extended. I have been through all the troubleshooting with verizon including a new sim card. Apple insist its a network problem but verizon can not resolve the issue. I would appreciate any help
I have had this problem for a year and thought I'd tried everything but I believe I've now fixed it. I turned off automatic carrier selection (Settings/Carriers/Automatic) and waited an age before it came up with the available operators (EE, Vodaphone, 3, O2). I selected EE and since then it hasn't once shown no service.
I hope this helps others.