I have the same issue and have tried numerous different sd cards, brand new batteries with full charge, taken trhe camera apart (every pcb disconnected and removed, checked all terminals and battery terminals, no faults found.
I have tried updating firmware (currently on v 03.02 and still it switches off and on constantly.
I have now decided to give up and my only solution seems to be a new camera and it wont be a GoPro.
Thank you all for your input :-s