I believe Dave is getting at rigid body motion when he says "when the connection slips." A displacement constraint is a load which directly defines the degree of freedom values on the nodes involved. So while rigid body motion is not allowed in a static structural analysis, and causes nonconvergence, it is allowed if that RBM is fully applied on the DOF by a displacement load. By the look of your model, it does not seem like it is a model with RBM, but any failure or slippage at the contact would allow RBM. So contact slippage can allow convergence when the load is applied as a displacement but not as a force.
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