Bit of a long shot here but I have a KP1 which keeps cutting out (appears to reboot) after a short time. Tried factory restore. Any ideas? Don't think it's to do with the power supply as it doesn't actually go off. Like I said, a long shot!!!!
I had the same problem with mine:
http://der-warst.de/warstware/kp1.html (http://der-warst.de/warstware/kp1.html)
Simple solution: get a stronger power supply. The original PSU seems to be too weak with 750 mAh. Once I tried it with a 1500 mAh one, the problem was gone for good.