Assuming that by "repaired" you mean patched or plugged and not just filled with sealant, then whether you replace the tire after a puncture is a judgment call. It depends on several factors: the age of the tire, remaining tread life, conditions of roads you drive on, type of driving you do. I wouldn't take a patched or plugged tire on a track day under any circumstances, but, strictly speaking, if a tire is otherwise in good shape, if it's a small, clean puncture, and if you drive moderately on well-maintained roads, then a competently-done patch or plug will last the remaining life of the tire. So IMO no, you don't need to replace a repaired tire.