Try disabling Auto-Schedule in the Nest app (per suggestion from another
user). When I did that, battery voltage jumped up to a range between 3.6
and 3.8 and has stayed connected for a week. The Nest "Learning"
Thermostat, 3rd Gen, no longer whines a...
Nest, Google and users owe you a big Thank You for tracking this issue
down. I disabled auto scheduling and my Nest Learning Thermostat has
been holding a charge for a week now.