Low power FreeBSD computer board needed

Hello!

Trying to avoid the recent battery overheat problem, I am looking for 
some small computer board that is able to do the following:

1) Compile from sources and start a graphic Youtube capable web browser 
under FreeBSD (Arch does not matter),

2) Sleep at least 72 hours being powered from 4 AA cells, with all 
peripherals except COM port powered down. In this mode the COM port 
input should wake up the system in less than 1 second.

Raspberry Pi is almost OK but it's power consumption in lowest power 
mode is 10 times higher than allowable. Saving Raspberry Pi state to 
flash and powering it down is 10 times slower than allowable (and kills 
the flash, too).

Can you advice me such a board?

Yours

Anatoly