Call and go through the motions of rebooting your modem and do what you can to get an on-site tech out.
Since your modem is flagged for recommended upgrade they may try to say it's your modem, but don't change it yet since it was working before and mention that on your call.
I upgraded mine due to their recommendation trying to get my connection fixed and it turned into a ticket and charge for a new modem install and the problem was still happening afterward. I had to call their billing department to get that charge reversed.
They may threaten to charge for having the tech out if the problem is on your end, but it does sound like the issue lies somewhere between the modem and Cox.
The on-site tech will probably replace all your lines and connectors.
If it's still happening after that, do what you can to request it be escalated with the on-site tech. The support chat and phone line is useless for getting anything but getting upsold services, a modem reboot and an on-site tech visit scheduled.