Over the last 36 hours, my Nest WiFi has dropped connection to my modem. Once I realize what has happened, I unplug the Nest and after a few seconds plug it back in. Most times, this solves the problem. I have 2 questions - 1. Why doesn't the Nest realize the loss of connectivity and retry periodically by itself and 2 - are there any logs I can extract from the Nest so I can see when the connectivity is lost?
It should detect when internet is gone. You can check what notifications you have enabled for the Google Home app.
To log when and for how long the internet connection goes out, you can set up some kind of monitoring on a client (PC for instance) connected to the network. Maybe something like "Net Uptime Monitor" (haven't tested it myself, so no promises):