Play5 Gen1 Cutting Out

Wifi extenders are officially not supported. Use real wifi or a mesh system.

Is there any reason you do not wish to leave the Ethernet cable connected if that solution works? Ethernet ports are there for to solve the exact issue you are having.

Since we do not know any other information about your network besides the fact that you have a wireless extender, I would suggest you look at this page for what Sonos suggested network requirements are:

https://support.sonos.com/en-us/article/sonos-system-requirements

As ​@controlav3 stated, a mesh network like an Eero system may work better for you.

Given the age of the PLAY:5 gen 1, there’s a possibility of a failed WiFi system in it. I’d connect it with the Ethernet cable so it shows up in the controller, and submit a system diagnostic , and then at your convenience call Sonos Support to discuss it. Don’t post the resulting diagnostic number here, Sonos’ lawyers get sensitive about GDPR, I suspect.

There may be information included in the diagnostic that will help Sonos pinpoint the issue and help you find a solution.

When you speak directly to the Support staff, they have tools at their disposal that will allow them to give you advice specific to your network and Sonos system.

Pools -3105 
The speaker is situated in a different room from the router. 

Airgetlam

Thanks for your suggestions 

If it is a failed Wi-Fi card Sonos may offer a discount on replacing the speaker as long as you haven't opened the case.