Use something like Xpra or NX: they both allow you to run applications on the screen of the X11 server, to which you can re-run, if necessary, from remote computers. They both support "seamless" sessions, so windows will appear just like local windows.
Practical example:
xpra start :10 --start-child=/bin/YOURAPP
Then, when you want to reconnect (say, after restarting the X11 server):
xpra attach :10
Or from a remote machine:
xpra attach ssh:THESERVERHOSTNAMEORIP:10
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