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Is the mount garmin's own one or something else from amazon or something?
I have two mounts and two etrexs and have never had a problem with these. I do have lanyard to be safe but it's never slipped from the mount even if I bottom out the fork on a jump or crash. But maybe I've just been lucky.
You could use rechargeable batteries, you can get ones with built in usb port, like these
Not quite as sleek as charging the device itself but can be better this way if it's raining.
Already have an etrex, it's great but it does tend to throw itself off my bars to the ground at first sign of any bumps. Ideally I'd like a smaller etrex with a sleeker user interface and a securer bike interface that could be charged via USB.
Upload a GPX and follow a line on a screen is all I really need.