An investigation of barrier endurance till electrical breakdown in MgO-based magnetic tunnel junctions (MTJs) is presented. Samples were tested under pulsed electrical stress. By studying the effect of delay between successive pulses, an optimum endurance of MTJs is observed for an intermediate value of delay between pulses corresponding to an optimum trade-off between the average density of charge trapped in the barrier and the amplitude of its time-modulation at each voltage pulse. A charge trapping-detrapping model was developed which shows good coherence with experimental results. The influence of the delay between pulses on the trapped charge density in the tunnel barrier and on its time-modulation is discussed. The average density of trapped charges and its time-modulation are, respectively, responsible for a static and dynamic stress within the tunnel barrier, both leading to breakdown. The probability of breakdown of the MTJ for different applied pulse conditions has been evaluated. The expected endurance of the MTJs was deduced depending on the characteristics of the electrical stress in terms of delay, and unipolarity versus bipolarity. The study emphasizes the role of electron trapping/detrapping mechanisms on the tunnel barrier reliability. It also shows that extremely long endurance could be obtained in MTJs by reducing the density of electron trapping sites in the tunnel barrier.