Dynamically cross-linked semiflexible biopolymers such as the actin cytoskeleton govern themechanical behavior of living cells. Semiflexible biopolymers nonlinearly stiffen in response to mechanicalloads, whereas the cross-linker dynamics allow for stress relaxation over time. Here we show, throughrheology and theoretical modeling, that the combined nonlinearity in time and stress leads to anunexpectedly slow stress relaxation, similar to the dynamics of disordered systems close to the glasstransition. Our work suggests that transient cross-linking combined with internal stress can explain priorreports of soft glassy rheology of cells, in which the shear modulus increases weakly with frequency.