It’s true that Sonos do not officially support WiFi extenders, as stated in their system requirements, but no doubt some WiFi devices out there may work. What you haven’t mentioned in your post though, is if you have added the new WiFi network SSID/credentials, (extended or otherwise), to your Sonos device. I would recommend you wire the Connect:Amp temporarily to your new router and add the new wireless network to it, via the Sonos App, using the instructions in this Sonos Support link…

https://support.sonos.com/en-us/article/connect-sonos-to-a-new-router-or-wi-fi-network

Once that’s done, ensure your extender is broadcasting the ‘exact’ same SSID and has the same password. I also recommend the router and extender use the same ‘fixed’ non-overlapping WiFi channels (1, 6 or 11 for the 2.4Ghz band) and the same 20Mhz channel-width for that band.

Once the new network has been successfully added and any changes made to channels etc; you can then uncable the Connect:Amp and allow it to run on either your ‘router’ or ‘extender’ WiFi signal.

Hope that’s easy for you to follow and that it gets the Connect:Amp back up and running for you.

Thanks Ken. I think this is above my pay grade! I’ll enlist the help of someone more technically advanced and let you know the outcome. 
 

I have changed the Wi-Fi in the connect amp to the new one, but only through the extender. 

Okay, if you continue to have technical difficulty with the setup described, it might be worth you perhaps calling Sonos Support Staff when you are near your system and have some time on your hands, as they maybe able to walk you through the steps. Here is their contact link if you perhaps want to give that a try:

https://support.sonos.com/s/contact

So, I took the connect amp down to the router, and reset it on the Wi-Fi down there and it found it. I’ve taken it back upstairs and it WORKS! 
 

Thank you so much, we have music again! 

My connect amp all of a sudden, after a few years, started to disappear from the system. I’ve followed the instructions for reconnecting, to no avail. Then, for some reason, it reappeared. And now it has disappeared again.

It was an expensive lesson, but I will NEVER buy any foggin Sonos products again. 

Without any further information from you, it sounds rather like an intermittent SSDP multicast device discovery issue between the Sonos device and controller - you mentioned that you ‘followed the instructions for reconnecting, to no avail’ - what steps were those exactly?

Did the device drop the router assigned IP address, or is the network up-time showing it was still connected to the LAN subnet?

Is the C:A your one and only Sonos device, or do you have other products in the same setup? Also what is the date of manufacture of your device (shown at the beginning of its serial number) as some C:A’s are quite old and by your own account, you’ve had it for some years.

So the interesting thing is that when I press the play button on the C:A, it plays music from a previous session. It does not show up in any streaming app, and I can close all streaming apps (Sonos, Spotify, Apple) and it still keeps playing. Where it streams the music from, I do not understand…

I also have two Ones and a Sub. They are always visible and I rarely (if ever) have any problems with them. 
 

Oh, and the instructions I have followed are those in Sonos webpage for reconnecting units to the system, including resetting it and the router etc. I once connected it directly to the router while reconnecting and that worked. For a while. 

From the recent information you have provided it does sound like a multicast device discovery issue - the fact your other speaker(s) always show up, lead me to think your C:A is either connecting to a different wireless access point, or its suffering from intermittent interference - if it is using a different AP, then simply blacklist the devices MAC address on that AP and see if that resolves the issue. If it’s interference, then perhaps see what is nearby or in-between the C:A and AP…

Another thing to try too, is if your controller device has MAC address spoofing enabled, then just see if disabling that may help.

One further matter that some users report some success with, is to perhaps check and see if UPnP protocol is enabled within your router configuration, some users have reported success with enabling that on their router. I’m personally not sure why that may work, but SSDP is part of the UPnP protocol, but it’s used for auto-port forwarding mostly between WAN and LAN - if it makes no difference after trying it for a while, then leave it disabled.

And finally, check the mobile controller for running software, particularly security software, like VPN, Firewall, Anti-virus etc; as those things too can affect multicast device discovery and see if disabling those things (if present) makes the non-discovery problem go away.

I hope at least one of the suggestions above, help you to find the answer.

Well, I bought the Connect amp together with the rest of the system, in 2018. Not too long ago, me figures. It should still be supported by Sonos, right? It seems my router is connecting the Connect amp to its 2.4 Hz band, and the rest of the Sonos gadgets (onex2 and a sub) to the 5 Hz band. I can see all four gadgets connected to wifi

and yet the Connect Amp pops up only intermittently in Sonos S2 app. 
They say it’s easy to use. For a while, that’s been true.

Is the 2.4Ghz band named differently. or the same, as your 5Ghz band? If they are named the same, perhaps try separating them (by giving the 5Ghz band a different name) and put all your Sonos devices, including your Sonos controller device, on the 2.4Ghz band and just see if that perhaps resolves your issue. My thoughts are that the router might be having some difficulty passing the multicast packets between the two WiFi bands. The suggestion here comes from seeing some BT routers in the U.K. which have had that difficulty in the past. It’s at least perhaps worth trying that and seeing what happens.

Thanks; I really appreciate the efforts to help.