Segmenting my network isn't an option when "my network" involves machines on multiple continents.
I avoided ssh because sshd is an effectively unauditable mess, and breaks the "transient network glitches don't kill quiescent connections" assumption.
How do transient network glitches kill the connection? I'm not completely familiar with the ssh wire protocol, but to my knowledge TCP is largely responsible for ensuring the reliability of the virtual circuit even in the event of a transient lower-layer failure.
ssh frequently uses either application-level or TCP-level keepalives. But it doesn't have to; you can just turn off ssh keepalives and your quiescent connections will survive network outages.