DIAGNOSIS It's a Wi-Fi band conflict. The 2nd Gen Nest Mini supports both 2.4GHz and 5GHz networks, but it can get confused if your router uses the same network name (SSID) for both bands.
FIX Log into your router's settings and temporarily split your Wi-Fi bands into two separate networks (e.g., "HomeWiFi-2.4" and "HomeWiFi-5"). Set up your Nest Mini on the 2.4GHz network only, as it has better range through walls and is more stable for IoT devices.
IF THAT DIDN'T WORK The issue could be IP address conflict. In your Google Home app, go to the device settings, find "Wi-Fi" and tap "Forget this network." Then perform a full factory reset on the speaker and set it up again as a new device, ensuring it gets a fresh IP lease from your router.
HEADS UP Avoid placing the Mini in a crowded spot near other electronics, microwaves, or metal surfaces, as these can cause signal interference that leads to drops.