@rpunkt if 3ma is your current draw while sleeping, you will quickly drain any battery or supercap. The "mini boost buck dc board" itself has a no-load current of 1.77mA.
Might look here for low-power libraries and design considerations:
http://www.home-automation-community.com/arduino-low-power-how-to-run-atmega328p-for-a-year-on-coin-cell-battery/
https://github.com/rocketscream/Low-Power
P
