You're not obligated to support anyone. If it closing wouldn't bother you then by all means go elsewhere.
But with larger groups of folks playing and having the attitude of "if one of us is banned, none of us will go there again" (a fair number of former Military types like me, so we tend to stick together)...
What were you doing to get banned?
In my case, I was the local "Press Ganger" for Privateer Press and TO for the Wizkids stuff (MechWarrior) running tournaments at several local stores... The one "less pleasant" store owner accused me of breaking some sort of exclusivity agreement by running things at other stores.. No such agreement existed, and I was NOT an employee of his... But his store, his rules, he banned me and that was that. So, not a big deal, but it DID mean that the groups playing those games went to the other store instead of his... Other guys had similar experiences with him and another local owner... For a while there were NO local stores we'd play in, but that was a while back...