Are you using the new "bitter coating" Duracell batteries? I've had problems with them in my bike power meters, and I realize this is not a firearm but it's an interesting data point. SRAM (manufacturer of the Quarq power meters), sent this update via email:
Battery compatibility notice
The newest Duracell CR2032 batteries are not compatible with SRAM and Quarq power meters.
Use of a Duracell battery with a bitter coating ring will result in symptoms similar to a drained or low battery.
These could include:
No wake or pairing possible
Loss of combined cadence and power for extended periods
No LED function
Duracell 2032 Lithium Coin Battery with Bitter Coating - bitter coating ring added as a swallowing deterrent.