For example, in nonlinear problems (e.g. contact interaction), it sometimes helps to reduce the load increment, i.e. to apply the load “more gradually”. Bring the master and slave into contact in several steps, then close and establish contact, then load as you please.
The same with plasticity. In this case, it may also help switching from load- to displacement-controlled mode. Changing or varying the yield criterion often helps as well.
If the reason for poor convergence is mesh distortion, it may, at least in theory, help to make the mesh coarser so that individual elements do not get distorted that much as strain builds up.
Finally, the easiest (and the first) thing to try is to set up the simulation with a smaller minimum time increment in the step that did not converge. This is often all it takes to make it converge (default settings are suitable mostly for problems with no convergence issues, e.g. linear elastic).