I have a pro mini in a datalogger powered from a 9V battery, the device also contains an LCD module (no backlight) powered from the 5 V line of the arduino. Is there a simple way to completely power down the device after, say 20 mins, of idle time. I am not bothered about waking again (they can just switch on and off from the power switch), the key thing is to cut the power to save the battery.
You can put the processor into power down sleep mode.
You need to add extra circuitry tho to disconnect from the 9V battery, otherwise the 5V regulator will keep on making 5V, even if just the power LED is using it.
My idea:
A pre-built possibility is the nifty pushbutton power switch circuit designed by Pololu. It has an "off" digital input, but a button push turns it on again Pololu Pushbutton Power Switch SV (old version)