I don’t own yet a nice multimeter, so the current measurement I did with my actual (too) cheap one is rather approximate. I got around 12mA with the LEDs on, and around 4mA in sleep mode, drawn from the battery. Maybe the current of the sleep mode is still high due to the step-up circuit, which runs all the time…

However it stays on at least 3 consecutive days on a single AA Ni-MH rechargeable battery. I logged the battery voltage of one candle with my raspberry-pi logging station. It start with a fully charge single AA Ni-MH battery and I remove the sleeping mode:

Using the 'day sleep' it's approximately 5 days one ~2Ah battery.