In reply to Michael O'Neil.

I thought more about my response, and I think the question you ask is hard. PROC ROBUSTREG in SAS is restricted to robust linear regression. PROC NLIN or PROC NLMIXED have the potential for Y-robust logistic regression (robust against outliers) but not X-robust logistic regression (robust against influential observations in the explanatory variables), which seems to be the case you are interested in. In the literature, there have been several proposals for robust logistic regression methods. One that has software is
Cantoni and Ronchetti (2001), “Robust Inference for Generalized Linear Models” and R package: glmrob.