I think you're just being paranoid and/or exaggerating. There's no reason a member should go to the trouble of logging out and back in 10 times a day from the same computer. Most of them have trouble remembering a single user/pass.
Don't spread the problem by implementing any kind of auto banning.
It's also possible there's some other problem entirely, but you're so convinced that so many members are doing this to you that whatever it is becomes impossible to diagnose.
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