Why does the breathing rate not return to normal after vigorous exercise?

During vigorous exercise, muscles are not supplied with enough oxygen. This means that cells have to respire anaerobically. Anaerobic respiration involves no oxygen. This leads to a build-up of lactic acid in the muscles and creates an oxygen debt. Lactic acid causes muscle fatigue and prevents muscles from contracting efficiently. In order to remove the lactic acid, it needs to be oxidised. The increased breathing rate allows more oxygen to enter the body and help to remove the lactic acid.