Time issues with 5c

MY wife has just brought a second hand 5c 16gb phone from cash converters. It all works fine except the date and time. It will not update itself and the clock is not moving. All location services are switch on and I have tried setting it manually. When I do it works for a few minutes and then stops. The phone did update to newest version before we restored it from a previous phones settings. Apple thinks it may be a hardware issue and suggests I take it back. Before I do, has anyone come across this before.

TIm