Electronic equilevant of latching relay circuitry

MarkT:
Yup, better circuit. But the latching on-switch is going to be more complex. You could have your
high-side PNP transistor (note its wrongly labelled in the Fritzing diagram as N) driven by
an NPN from ground. Then when the power is off, the Arduino pins at 0V won't turn on the NPN.

I'd personally just use a CMOS RS flipflop that's permanently powered to drive the switching device,
that's very flexible and CMOS uses a few nanoamps quiescent so no issue with battery life. Have the
accelerometer set the flip-flop, let the Arduino reset it to power off again. No worries about race conditions.
A CMOS flipflop can also be constructed from 2 NAND gates or from two NOR gates.

Thank you once again for your help MarkT. I'll follow your advise on flip-flop.
Cheers.