Wow! I'm much obliged for the plethora of great responses. It's a good lesson: phrase your request succinctly and you'll get a better response. Thanks.
So to summarize helpful ideas I got:
- Connect a relay on the power line.
- Use AA or AA batteries.
- Use a flip-flop
- Latching relay to sustain power until Arduino comes up
- The pololu proprietary solution
- Remove all power draining stuff and just put the Arduino in a sleep state
- 555 timer to sustain power
but my favorite, and the one I think I'll try first (I'm extrapolating here)
- wire up an off-center motor that, when activated, knocks my little box onto its side, turning off BroHogan's mercury tilt switch.
Seriously, though, thanks Bro, and thanks for the latching circuit diagram. As a SW guy it will probably take me a day to understand how that works, but I am determined to figure it out.
Thanks, all!
Mikal