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

Ahh - it could well be a battery issue - keeping the radio receiving all the time takes up quite a lot of power. I just measured and it's around 12mA - so if findDevices were on constantly it'd drain a 200mAh battery in 16hours. It's still some way off your 8 hours running it for 1 in 4 seconds, but it could explain a lot.

CR2032s don't like high current draw, so it's possible that it would die and then come back enough to boot into an unprogrammed Espruino environment.