Iphone 5c disconnects when restoring

I need to restore my phone from a backup I had made. The problem is that it will disconnect and reconnect real fast at 2 certain times. Sometimes it'll do it at the first sync when it's first connected to the computer and the second time is during the restoring process. I know it's not the cable since I have tried it with a brand new USB cable. But here is the following message I get every time.