Which voltage regulator should I use? A friend and I are working on building a smartwatch on a budget, so it’s a (very) low power project, but we are currently having a problem with the power supplying.
We already chose this board, because of its size and the BLE chip: RFduino BLE SMT
For now on, we are planning to use this battery 500 mAh LiPo battery (approx. 4V at full charge) with this voltage regulator Micrel MIC5209-3.6YS (the board supports 3.6V max.).

But the problem is that the Voltage Regulator will apparently drain by itself too much energy from the battery (by heating), reducing drastically the autonomy.

So we would like to know if you guys can help us, if you can tell us exactly what (type of) regulator would be the best or if we need to find another battery.
IGND which is mentioned on page 4 of the datasheet is apparently proportional to the output current. This accounts for about 2-5% of the total current drawn by the regulator, depending on its load. With the maximum voltage drop of 4 - 3.6 = 400mV, a switching regulator will make no real difference. I think your only option is to find another regulator that has better efficiency.