Thanks for your reply and I am sorry for the delay.
The Nest thermostat will be disconnected from the Wi-Fi for a couple of reasons. First, if the battery is not getting enough power to charged, it will be disconnected from the Wi-Fi to conserve it. Second, the location of your thermostat. There are electronic devices that might be the cause of interference. Another thing is the common wire (C wire). Do you have a C wire connected to your thermostat?
You could check this link to know more about your Nest thermostat battery status and how to manage it.
I hope it helps.