The battery life of a thermostat depends on a few factors. Verify the following if a thermostat is experiencing short battery life.

Verify the thermostat uses recommended batteries

It is recommended that all thermostats use high-quality, brand name, alkaline batteries. Verify the thermostat is using the recommended batteries with a strong charge. 

Verify the thermostat enrollment

There may be issues if the thermostat was enrolled using AC power but now solely relies on battery power. If the thermostat has a C wire, verify this by removing the batteries, placing the thermostat on the wall, and attempting to press a button. If it doesn't light up, the C wire may not be connected properly.

It can also help to delete and re-add the thermostat off of the wall to make sure it enrolls on battery.

Z-Wave communication issues

When Z-Wave communication is poor, the thermostat uses more power attempting to connect to the controller. Verify that the thermostat has a consistent Z-Wave connection.