We report an experimental demonstration of period doubling of dissipative soliton resonance (DSR) pulses in a fiber laser. DSR occurs in the close vicinity consisting of a set of parameters of a dissipative system, where the energy of the generated soliton increases without limit while the pulse peak power is clamped. Consequently, DSR pulses are immune to the appearance of period doubling, which is a threshold effect. However, period doubling of DSR pulses is experimentally demonstrated and numerically duplicated. The typical DSR feature, i.e., clamped pulse peak power and linear variation in pulse width with respect to the pump power change, is lost during the transition from period one to period doubling. However, the DSR performance reappears once the period doubling is fully developed. The breach and recurrence of DSR operation during pulse evolution results from the simultaneous change of multiple parameters because of the increasing pump power. In addition, DSR pulse narrowing with pump power increasing under the period-doubling state was experimentally observed.