After searching the internet I have found this thread on here.
Im having the exact same problems. I have good signal but when im at work at my desk I lose signal. The first time I noticed this was when I arrived home and noticed that I had "no service". I just ignored it at first and after 20 mins I still had no signal (I normally average around 4 bars signal at home). I decided to switch the phone off and back on and then didnt think anything of it. Then the same happened again the following day and so on... The phone gets stuck on the "no service" until i restart the phone.
Im very annoting by this, I never had this issue on my iPhone 4 and although the iPhone 5 is a great piece of technology it doesnt actually serve its purpose... afterall, it is an iPHONE. I have missed about 20 calls in total and a good amount of texts because of this issue.
I phoned apple who adviced me to reset network settings, this didnt work. They then said restore the phone, this didnt work. They said get a new sim card, this also didnt work. They said start the phone as a new phone, and it still doesnt work.
I was in two minds about buying this iPhone and to be honest, I shouldnt have bothered buying it. Im visting the genius bar at my local apple store next week, not sure what they will do but obviously, this is an issue that Apple need to sort out and QUICK!