I don't know yet really. I just got my first tama yesterday. I don't play games very much, just when my tama isn't 100% happy and sometimes when im REALLY bored.
The first time I start a Tamagotchi (w/ the battey it comes w/), the battery usally lasts about 2-3 months. After the battery runs out, I put in Lithuim Batterys, wich usally last about 4-6 months.
Most of my tamagotchis run out of batteries when they are an adult on the 6th generation. So that would be about 2 months.
The ways to save power on your tamagotchis are keeping the sound turned off, playing games and connecting. Those are the 3 main things that use up your tamagotchi's battery.
P.S. This topic should be in the "What's on your mind?" section of tamatalk. I will contact a guide to move it. Remember: Always check that you are posting your new topics in the right forums. It will save people getting confused and it will make less work for the guides.