Intermediate filaments are cytoskeletal proteins that are key regulators of cell mechanics, a role which is intrinsically tied to their hierarchical structure and their unique ability to accommodate large axial strains. However, how the single-filament response to applied strains translates to networks remains unclear, particularly with regards to the crosslinking role played by the filaments’ disordered “tail” domains. Here we test the role of these noncovalent crosslinks in the nonlinear rheology of reconstituted networks of the intermediate filament protein vimentin, probing their stress- and rate- dependent mechanics. Similarly to previous studies we observe elastic stress-stiffening but unlike previous work we identify a characteristic yield stress s⇤, above which the networks exhibit rate-dependent softening of the network, referred to as inelastic fluidization. By investigating networks formed from tail-truncated vimentin, in which noncovalent crosslinking is suppressed, and glutaraldehyde-treated vimentin, in which crosslinking is made permanent, we show that rate-dependent inelastic fluidization is a direct consequence of vimentin’s transient crosslinking. Surprisingly, although the tail-tail crosslinks are individually weak, the effective timescale for stress relaxation of the network exceeds 1000s at s⇤. Vimentin networks can therefore maintain their integrity over a large range of strains (up to ⇠1000%) and loading rates (10−3 to 103s−1). Our results provide insight into how the hierarchical structure of vimentin networks contributes to the cell’s ability to be deformable yet strong.