[Nextgrid]

Nothing to do with Wi-Fi, the same would happen if you had 2 Ethernet connections.

Your Wi-Fi and Ethernet are both network interfaces with their own IP addresses - those addresses don't move when you switch between interfaces. If you established an SSH session while on Ethernet and then unplugged it, that session will not carry over to Wi-Fi unless you change your Wi-Fi interface's IP address to the wired one's and that both networks are on the same L2 segment (typical for home networks, but not always the case for enterprise).

A potential solution is either MPTCP (which will establish multiple connections over all interfaces and can tolerate the loss of all but one of them) or to VPN into your router and use the VPN link as your default route - this means that the VPN connection might drop and reconnect but your IP address to the other hosts (which is actually the one of your VPN gateway) will remain constant, so traffic flow will be restored as soon as your VPN reconnects even if your local IP changes.

[fulafel]

In internet design circles these themes are known as multihoming and the locator/id split problem. See eg https://labs.apnic.net/presentations/store/2004-07-27-multi6...

Also IETF's envisioned post-TCP transport protocol (SCTP) supports multihoming natively but has failed to take off.