That's my point. If you select a low current relay or P-MOS option, a screen with a low-power mode and a switch(or gesture sensor) on the backlight, and an Arduino on low power mode then there's no reason you can't stick a couple 18650s in there and call it a decade.
Or follow what @johnwasser suggested and use 2 Arduinos and repurpose your wiring; that's a no battery solution.