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Seems unlikely as long as you remain in good standing. What bank?
I would think in most cases the explicit language is on restrictions on opening the account, so once that is done no more checks are done. Now it doesn't make a lot of sense (if for some reason geography is important at the time of opening it should probably remain so) but whatever.
And also sometimes banks don't do the checks anyway. I have an ISA with a UK bank and discovered after a year or so that the law requires this is only for UK residents (as it is tax advantaged). I have continued to forget to point this out to them, must do it soon!
I moved out of BofA's and Wells Fargo's geo-locations without any problems.
After a couple of years, they were both closed by me. For better banks.
A former geo-restricted bank did not shut me down after I moved ~2,000 miles, eventually I did close the account.
My two main banks are georestricted. One of them actually states that some of their products (auto and home loans) are also georestricted, but that's it.
There may be exceptions, but most regional banks/CUs will allow you to keep your accounts/membership even after you move.