Factory resets are almost never the answer. They also erase any data on the speaker that might help Sonos figure out what was going on. 
 

Have you read the  LED states FAQ?

At the very least, I would recommend that you submit a system diagnostic and call Sonos Support to discuss it.

There may be information included in the diagnostic that will help Sonos pinpoint the issue and help you find a solution. Especially if there might be a hardware fault with the LAN card. 

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

Thanks Bruce - yes have read the LED states, but I can’t see that explains. Will run the diagnostic like you suggest - thanks.

@paulC_

In the instance where the C:A was displaying different LED colo(u)rs, that description sounds the same/similar to the Diagnostic snapshot state, where a full system report is dumped for submission to Sonos, but then you go onto ‘factory reset’ your device and get a white flashing LED - which is not the correct display for a device ‘reset’. The LED should flash Amber and then go onto switch to a flashing green. 

A flashing white LED often means the device is not factory reset, but merely seeking its last network connection and IP address.

If it’s your only Sonos product, I would suggest you first wire the Amp (again) to your router and restart it and see if it then shows a steady white LED, next open the Sonos App and see if it appears in the App.

Then report back here before taking any further steps.

It would be helpful to also know at that point too, if you have more Sonos products, in your Sonos system besides the Connect:Amp?

I have 4 other Sonos components: another sonos connect amp, a sonos connect, and two beams.

 I have tried connecting to the router - doesn’t change anything that I can see - still white flashing light and not showing in the app.

Hello,

I have 3 connect amp. i had the exact same problem in two of them. From one day to another they disappeared from the system on the app. I previsously fixed the ip adresses so that they don’t change over time. I’ve done that from the router by linking MAC with IP. It worked fine over years. 
So on those two units, white led is flashing very slowly, I removed the link Mac/ip, tried again, set it up again, tried again, reboot router, reboot power, nothing worked. I hard reset one of them, I got the orange light indicating it reset, green and added it to my system as if it was a new one. It worked perfectly! However, the second unit refuses to accept tte factory reset procedure, it seems to do nothing as if the buttons were not working. I even let the unit over night disconnected from power and tried again the morning later to reset (hold play button while plug the cord and wait ….. waited even 60sec and nothing). I tried also with play button + volume up. 
I assume the unit is defective….I hope I’m wrong and can fix it easily. Any help would be appreciated, please.

If you suspect a defect, stop trying to reset the device and call Sonos.

Did you fix it?