That would be in the SSH client's configuration and unrelated to the infamous systemd, though scope creep might see that change in future versions. See instead "man ssh_config" for the ForwardX11Timeout directive which defaults to 20 minutes. The manual does not say but I suspect that if it is set to 0 then X11 is allowed indefinitely.
However, the launch is done incorrectly. If you would like the client to go into the background, use the -f option:
Code:
ssh -f -X -l pi 10.1.1.91 "midori &"
Then the ampersand (&) will be optional. Either way, mind the quotes.
You may also be interested in ServerAliveCountMax and ServerAliveInterval.
Some settings can be made permanent in ~/.ssh/config:
Code:
Host 10.1.1.*
User pi
ForwardX11Timeout 0
ServerAliveCountMax 3
ServerAliveInterval 15
Host *
TCPKeepAlive yes