Mesh size decrease making time dependent model not converge for as long

I’m running a time dependent model of ice deformation. Generally, I've experienced smaller mesh sizes improving results. However, I’ve recently been encountering some situations where a finer mesh is causing a time dependent model to not converge over as long a period of time. For example for the attached model, with a coarser mesh it will converge up to about 600 years, while a coarse mesh will converge to 250, and a normal mesh will converge only to 140. I'm using COMSOL's default solver settings, which have generally worked well for me, including in similar models. I'd appreciate any suggestions on what I might try to fix this problem.