My iPhone 5 clock stops working when I lock the screen. Any solutions?

I have tried to find a solution, but no one has seemed to find one yet. The clock on my iPhone works just fine when I'm using the phone, or when I'm charging it. But every time I lock the screen, it just stops. The Wi-Fi connection is also bad, and the GPS is not accurate. I have tried to:

Turn it on and off.

Adjust the time manually and change the time zone.

Take the sim-card in and out.

Reset the iPhone back to factory mode without adding anything new to it, which I think is strange that it didn't work.

I have also contacted the operator, who claimed they never heard of the problem. I have read about several different people who had the same problem, but no one found a solution. Please help? I don't want to buy a new phone just becouse of the clock.