Is the Sonos Arc wireless, or wired (is it using SonosNet?) and have you checked that it’s WiFi adapter has not been switched off?

Also note you must use a mobile, not desktop, controller App, which should meet the system requirements shown here for the S2 App:

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

I would also ensure the router WiFi is 802.11b/g/n backward compatible and is perhaps using security mode WPA2 Personal (AES).

You may perhaps find this link helpful too, which shows the Sonos System Requirements:

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

The app says that the Sub is connected but no sound is coming from it. Also, it said it was connected, THEN said it was not connected — multiple times; I have gone through the connection process multiple times. 

That suggests a couple of potential issues. First and foremost, some sort of wifi interference impacting the 5Ghz range, somewhere near either the Arc or the Sub. The Sub does connect to the Arc, and not directly to your router. 

Another potential issue could be duplicate IP addresses. The Sub receives its IP address through a proxy from the Arc, but if your router has multiple devices assigned to the same IP address in its DHCP table, they could be connecting/disconnecting repeatedly. Simple test for that would be to unplug all your Sonos devices, then reboot your router. Give the router a couple of minutes before plugging in your Sonos devices again. And if this does the trick, I’d encourage setting up reserved IP addresses for your Sonos in the router, check the router’s manual on how to do so. Any router that has gotten into this state once could conceivably do so again, reserving IP addresses is just good housekeeping, and will help keep this issue from reoccurring.

If neither of those fix the issue, I would recommend that you submit a system diagnostic within 10 minutes of experiencing this problem, 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.

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 network and Sonos system.

Problem resolved. After I rebooted the sub properly, it connected. Also, part of the problem was my hearing deficiencies and placement of the sub. After I touched the  face of the speakers in the sub, I realized that they were iindeed working, but to my ears, it sounded like the base was coming from the arc! ‍♀️ After I got it connected, I moved it from the tile floor to a piece of furniture near a corner and messed with the settings. It’s definitely working now. I also did the two automated room tuning processes. The light on the sub was going out because the Light Status parameter was set to off. I’m new to this, so I guess I just had a bit of a learning curve. Thanks!

It really is amazing, when dealing with Sub type frequencies, how much difference there can be by moving the Sub a few inches.