Just continue the same analysis for another few hours. When convergence fails, take more substeps and make the elements smaller as necessary to continue convergence.

There are lots of tweaks that can be done on the Frictional Contact Details to help it out.  You also should put in the Command Object


This will tell the solver to keep trying for 100 iterations before doing a bisection. Without that it will bisect in 26 iterations or less.

You are waiting longer than necessary by using small elements along the entire boundary. You only need small elements where the contact is occurring. Use large elements everywhere else.

You can also change the square to be a rigid part, then you won't get a mesh on the interior, only on the surface, but you have to use a joint to keep it fixed (or moving as the case may be).