hello i have the same problem But it was hardware the mainboard ! first restore the iPhone and set it, like new one ! if it still doing strange stuff about time reflow the GSM IC 350°c for 2 minutes my problem with this iPhone 5c : when the phone is off or when the screen is off the time stay where it was and never get back in the real time ? the time is working properly when the screen is on see you folks

hello a lot of things could be your problem ( dead battery oxydation dock anything else ) try to take it out from recovery mode via tiny umbrella and come back

and dfu mode to restore your iphone