Hello,
My assumption is that your battery is not a genuine apple product. That said, you may have an '''mAh''', means milliamp hour, issue and its forcing the voltage regulator to reboot the circuitry. Double check that specification, just speculation. Therefore, try placing the old, original, battery back in the device, use DFU and restore your last backup from iTunes. Then, trade it in for a newer device thru apple trade in program and receive something for it. Hope this information helps a bit. Good Luck!
Mike the IT Guy