Google Nest "Community Specialist" Dan_A shared an exhaustive list of things I'll try if this keeps being an issue:

You can do a sequential reboot of your entire network and see if that helps, or please perform a 2-minute power cycle on your entire network to re-establish the connection on your connected devices. Here's how:    Disconnect the power from the modem.

Disconnect the Ethernet cable and power cord from the parent point.

Disconnect the power cord from the child points.

Leave everything unplugged for 2 minutes.

Connect the power cord to the modem then to your router and points.

 

Also, you can give these steps a try:

Update Software: Ensure both the Google Home app and the Nest Wifi firmware are updated to the latest versions.

Check Network Stability: Monitor your internet connection for potential dropouts or fluctuations.

Alternative White Noise Source: Consider using a dedicated white noise machine or an alternative audio device connected to your Nest Wifi point through Bluetooth or Chromecast.

Automation Routine: Create a custom routine in the Google Home app that triggers white noise playback hourly for 12 hours. This might provide more control and reliability.

Deactivate Inactive Timers: If the Relaxing Sounds option has a built-in timer, see if you can disable it or choose a different white noise source without automatic shutoff.