Nest Learning thermostat power issue

I live in MN and installed the Nest 3rd generation thermostat in 2021. The power went below 3.7 volts last April and disconnected from the internet so I installed a Google Power Connector as we don't have a C wire. I obviously made a mistake wiring it as it discharged down to 3.6 volts two more times with the latest happening a few days ago. I'll review my wiring again but I'm going on vacation soon and wondering if it falls below 3.7 volts while I'm away--will just stop working completely or will there be enough power to at least keep the furnace running? My concern is with all the weird weather it could certainly get really cold here while we are gone. Any/all thoughts appreciated.