system is exactly singular

When trying to fit a generalized linear mixed model using glmmPQL:

fit0 <- glmmPQL(ifelse(response=="A",1,0)~gender,data=set1,

    random=~1|subject,family=binomial)
iteration 1
Error in solve.default(pdMatrix(a, fact = TRUE)) :
        Lapack routine dgesv: system is exactly singular

Could this be occuring because the paired responses for each subject are
always the same? If this were the case, what would be the best way to
handle this situation?

I replaced the response variable with fake data that are not always the
same for each pair and then I don't get this (or any) error message.