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The issue that you are having is related to the battery not holding a charge and would require the battery to be replaced. Since this is outside of the 1 year warranty, it would be cheaper to purchase and install the battery yourself rather than have Garmin perform the repair for you.
The battery replacement kit can be purchased here: https://www.amazon.com/Garmin-Edge-1000-Replacement-Installation/dp/B01LWOPQ1G
In the kit is the instructions on how to replace the battery along with the battery.
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