@sharpy Theoretically it can be done for the processor for sure, but you will hit problems with radio which is less amenable to low voltage.
You only really need remove the power LED for the pro-mini as that runs continuously, removing the VR requires external voltage source and control, tinkering with the processor speed and fuses (google here if unfamiliar) enables the processor to run down to very low volts with restricted performance, all well documented here and elsewhere, but as previously commented, radio may prove the greater problem.
My selected 16MHz 3.3v Arduinos stretched available performance to the limits, and no regrets, 100% reliable all the way down to sucking the batteries dry.
You may be better skilled than I to try, info aplenty here to assist from those who've been there and done that...
