I has the same exact problem. I was connected then oneway I woke up to a message saying it is offline. I guess it tries to keep on pinging the new Google Server. I reset the network, did not work, I reset the thermostat gen2 again did not work, the support person had access to the same problem solving checklist that Google has...nothing more...if they cannot resolve the connection and if you are under warranty they will simply send you replacement which again is not guaranteed to work...the Thermostat is not at fault, in my case, as it works fine offline..fingers crossed ...so far....am frustrated as I had spent hours on the phone speaking to the Technician from Honduras.
You are not alone...this happened after migrated from the Nest to Google....it is probably the google server that is causing issues...my internet works fine including my other Wifi devices...let's hope Google fixes this issue soon...
