Just to answer your question, my S1 system is working okay, so it maybe something you have done.

When you mention ..."I have tried resetting individual systems - to no effect”. Do you mean that you factory reset some/all of your devices?

Have you installed the S2 App at any point on any of your controller devices?

Have you tried wiring a non-reset Sonos device to your main router preferably a device that is S1(system) compatible only ..to see if that device shows in your S1 App when you attempt to connect to the existing system? (Please do not create a "new system" by the way, as you will risk losing all your settings/original setup).

By reset, I mean power-cycle - no effect.

I did do a reset on an Android S1 controller - no effect.

I have the S2 controller installed on a Win 10 laptop - it shows the system not found message too.

I have not updated any of the Sonos software or controllers on any systems.

I have tried the S1 controller on all  my local WiFi networks (I have 4)  - no difference on any.

Problem solved.

I reset (power-cycled) a bridge that is hardwired to my router & all systems came back.

That was weird.

The BRIDGE is an old device, and known by many users on this forum to have a dodgy power supply at this age. Which makes tracking down issues a bit challenging. I’d encourage you to either replace your BRIDGE with the newer and more robust BOOST, or wire your ethernet cable directly to a speaker. Or, honestly, you could just have your speakers on your own WiFi signal, as discussed in the wired and wireless modes FAQ.

I keep getting asked to update to S2 but I cannot afford to at present and anyway the sound quality of my S1 speakers is marvellous. I do not understand a lot of the tech speak but I do know that the last time I was asked to upgrade to S2 I couldn’t do anything until I accepted hoping it would still work my S1 speakers. Nothing works now!