You need to work out the necessary battery capacity. Find out the average current draw (measure with
a multimeter ?), decide how long you want to run it for and compute the minimum battery capacity.
Capacity = current x time.
Normally we use amps and hours or milliamps and hours - thus the units are either Ah (ampere-hour) or
mAh (milliampere-hour). Rechargable batteries should have a capacity spec, often printed on the battery.
But note the marked capacity is only true for a brand new battery that's correctly and fully charged and
discharged at the 10-hour rate - in other words add a healthy safety margin (50 to 100% - battery capacity
reduces with age and use).
So for instance an 80mA load for 2 days = 80mA x 48h = 3840mAh (3.84Ah). A 5Ah or 7Ah battery would
work for this case.
[ note AA rechargables are in the 1.5 to 2.2Ah range, typically - for more capacity C and D-size cells may be needed, or a SLA