If the alternator check out good and the belt and wiring are ok, Look at the damper pulley on the front of the crankshaft. A common problem is the rubber pulley mounting goes bad so the pulley slips on the damper. Symptoms are very much like a loose alternator belt. Easy to tell. Mark a line on the pulley and damper with chalk, paint marker or silver sharpie. Go for a run and check to see if the marks are still in line.