Enter: The Frame
This is GoPro's answer to this problem. Now you can shoot while being connected to an external power source. But, wait, $40 for a piece of flimsy plastic (to be fair, TWO pieces of plastic!) with a few holes in the side? No Thanks.
I really wanted this capability, but didn't want to spend a lot of money or sacrifice the poly case by drilling a hole in the side.
Enter: Modify a Mini-B USB Cable to Power an Enclosed GoPro Hero3 (With Skeleton Back Door) (This Instructable)
Disclaimer: Perform this at your own risk, I take no responsibility for your actions and assume you have some competency. With that being said, this instructable is merely a cable modification, I do not modify the camera or case.
Step 1: Parts/Tools
-A Mini-B USB cable of your desired length. I found an old 3-footer in my spare cables tub. I might suggest not using the one included with your GoPro (just in case...). Note: I have a Hero3 Black Edition which uses a Mini-B. I do not know what the Hero2 (or whatever) uses. Also, of course, your cable design may be slightly different.
-Glue...? I used some, it may not be needed though...
-Wire Strippers/Cutters. Not that you will be stripping wires explicitly - but you will need to cut off the black plastic molding around the connector and trim back the cable sheath.
-Long Nose Pliers. For general dismantlement and metal bendage.
-Small Rotary Cutting Tool. I use a really cheap one from Harbor Freight. Yes, it is cheaply made and doesn't have a lot of power, but hey its like $10 on sale.