You can estimate battery life by knowing the capacity and the power drain; in my case the battery was a 3.7V Li-ion, rated at 1100mA-hr.
If there are 4 nixie tubes, drawing 2mA at 160V, then each tube requires 320mW. Which means 4 tubes will need 1.28W.
The battery above is about 4 watt-hours of capacity (3.7V x 1100mA-hr = 4070mW-hr), so at 100% efficiency, the clock would run about 3 hours of continuous display time.
The demo board for my nixie watch ran for about 6 years on a single charge because I rarely turned on the display. And that was with a well-used cellphone battery, so it certainly did not have the full 1100mA-hr capacity.