Active mode‐locking of a laser diode in an external cavity has led to the observation of new instabilities. We report period‐doubling manifested by the alternation of weak and strong pulses in the mode‐locked laser pulse train. We also report period‐quadrupling where four successive pulses have different amplitudes. These results are attributed to the imperfect antireflection coating of the semiconductor chip, the latter constituting a regenerative amplifier with a time‐dependent delay for amplification. A qualitative analysis is proposed and validated by numerical simulations from a diode laser rate equation model.