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Say you get the privilege of 'creating gallery chat rooms' at 1,000 reputation, but lose enough reputation to go below 1,000 reputation, would the privilege awarded at that amount of reputation, be stripped off you?
Yes. So to take you as an example, if you have 1250 points and bountied a question for more than 250 points, you would no longer have access to the 1000 point privileges.