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Do you lose privileges if you lose reputation (e.g. by spending it on bounties) and dip below what you had to reach to gain that privilege? Or, do you get to keep a privilege once it is earned no matter what?
You must maintain a privilege's rep requirements to maintain that privilege.
Badges work a little differently. You always get to keep a badge, once earned. However, if you lose the requirements for that badge, your next badge earned in that badge category is a "makeup" one.