Hi,
If your switch-on time is 12 hours/day, then total on time for 30 days is 12*30=360 hours, right?
Your battery is 1000mAh, it means that it is able to supply 1000mA for 1 hour or 500mA for 2 hours or 100mA for 10 hours etc, now understand the pattern? (Multiply the mA with the hour, to always get the battery capacity.)
So now if you divide 1000mA by your needed 360 hours you can get the max mA value your circuit is allowed to consume: 1000/360=2.77mA from your 1.5V*3 battery.
unkarc