Can spraining an ankle permanently damage it?

Possible: If its a bad sprain and didn't get correct treatment it can lead to chronic instability so it would give out on you just walking. Also can cause cartilage damage like osteochondral defect.

IT DEPENDS: Most commonly, the outside ligaments are sprained. There are three. Sometimes one, or two, more rarely all three are, affected. Depending upon the severity, and how it was treated afterwards (yourself vs. a dr.) will dictate if permanent damage occurred. Sincerely, Dr. Latva

Multi factorial...: Although the severity of the injury is the obvious topic of consideration, conditions like age of the patient, blood supply, general health and physical fitness also play a big roll in whether or not the sprain as any permanency.