GoPro Hero 3 Black Edition

We took my son’s GoPro Hero 3 Black Edition skiing for the first time this Christmas. The camera was an Easter present from last March, but it took him a while to find interest in using it. It had not seen much use at all. So here we are in <10°F temps and the camera freezes after 2-3 minutes of recording. It just stopped recording or responding to button presses, and the only way to turn it off was by removing the battery.
Back at the inn I researched the issue and found that other people saw an improvement of these symptoms after a firmware update. So I downloaded the latest firmware (3.03), put it on the (Sandisk Ultra) SD card, and turned the thing on. That was the end of it. Since then all it ever does is turn itself on and off again after 3 beeps, forever.

The camera is technically still under warranty, but based on the chatter in the support forum and the reviews on Amazon.com I expect the worst from here on, i.e. support being slow to respond (so far I have not heard anything back), being sent equally defective replacement units and this becoming a bottomless time sink without us ever having a working camera again.

I tried different cards, I reformatted the card on my PC, and I downloaded the firmware again. Same results. It does not start up properly anymore, whether I am doing a firmware update or just in normal operation.
While it worked, it took great pictures.

There are now hundreds and hundreds of negative reviews on Amazon with complaints about a variety of unresolved issues with this camera. The GoPro support staff must be hopelessly overwhelmed with requests for an exchange like mine, and there must be a serious impact to their bottom line by now. Clearly, replacing frustrated customers’ broken and returned cameras with someone else’s broken and returned camera will in the long run not be a viable business model. This has been going on for at least a year now, and I am wondering if GoPro will be the next action camera manufacturer of the past.