In this study, we conduct a numerical evaluation of the impact of the recovery time of a saturable absorber (SA) on the output performance of an Yb-doped fiber laser operating in the dissipative soliton regime. Particularly, we evaluate the output pulse characteristics, such as the pulse width, spectral bandwidth, pulse peak power, and pulse energy depending on the change in recovery time. Applying a too-slow SA recovery time above a certain critical value is shown to make the output pulse unstable and broken. Furthermore, we demonstrate that there is an optimum recovery time range for stable dissipative soliton pulse generation, depending on the cavity dispersion and modulation depth of the SA. Further, we perform an additional numerical simulation of the pulse compression to demonstrate the relationship between the output dechirped pulse width and SA recovery time. The optimum approach for the generation of the shortest dechirped pulses in the dissipative soliton regime will be to construct a fiber laser cavity with a small normal cavity group velocity dispersion and use an SA with an appropriate recovery time.