This device was affected by the contact corrosion issue too.
Covering the middle 2 contacts stops the corrosion happening in the first place, but it has to effect on charging.
Please could you post a picture of the contacts? Have you tried cleaning them in any way? If it's not charging I'd say that'd probably be the first thing to try.
In terms of the battery life, had you tried installing the latest firmware and resetting everything to factory? While you can get 4+ weeks with default settings it's pretty easy to get the battery to run down a lot quicker by installing apps that use the battery more, or changing settings that use the HRM or things like that.
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Covering the middle 2 contacts stops the corrosion happening in the first place, but it has to effect on charging.
Please could you post a picture of the contacts? Have you tried cleaning them in any way? If it's not charging I'd say that'd probably be the first thing to try.
In terms of the battery life, had you tried installing the latest firmware and resetting everything to factory? While you can get 4+ weeks with default settings it's pretty easy to get the battery to run down a lot quicker by installing apps that use the battery more, or changing settings that use the HRM or things like that.