Is there a way to make the Puck more resilient to programming errors when running for a long time? Automatic reboot?

Yes, absolutely. There's some info here: http://www.espruino.com/Puck.js#power-consumption

Basically advertising uses very little power - it's only using the radio for a fraction of a millisecond, every 300ms. When you have a connection, it uses the radio more often = more power, but you can use NRF.setLowPowerConnection(..) to use a slower connection speed that uses less power.

It's really only things that keep the radio or CPU on for a long time that use the power (plus the LEDs, obviously). If I'm honest I didn't realise that findDevices drew as much power as it does!