(I have an actual end-to-end-connectable public IP from my ISP, which from the general discussion seems like an increasingly rare thing --- they keep pestering me to "upgrade" to outrageously faster yet slightly cheaper plans with a "free router included", so I suspect they are trying to get me to give up that IP...)
The other issue is ISP provided gateways that handle authentication onto the ISP network, like ATT fiber. These devices contain the certificate/keys to gain access to the network. Unfortunately theses devices also try to be more than just an auth device/gateway. In ATT’s case the gateway also handles some Uverse/IP TV services so they don’t have a true bridge mode where they send all traffic to another device. This approach then causes issues like update downtime or NAT table issues.
Either of these issues shouldn’t be caused simply by an ISP provided router. If an ISP wants to implement either approach they will do so without your approval.
This is true. Your options look like:
1. Get a new ISP
2. Get a VPN that supplies you with a public IP (these exist)
3. Hope you can do whatever you need on IPv6 instead
I had the same SSH dropout problem, asked my ISP[1] to switch me from CGNAT to dedicated IPv4; they did, and it's fixed.
[1] Aussie Broadband, a smaller ISP in Australia renowned for good customer service.