Logistic Regression implementation does not converge
This has been asked, and answered, on CrossValidated. See https://stats.stackexchange.com/questions/11109/how-to-deal-with-perfect-separation-in-logistic-regression and https://stats.stackexchange.com/questions/45803/logistic-regression-in-r-resulted-in-hauck-donner-phenomenon-now-what for two related answers (and there are other related questions that you can explore there). That logistic regression can blow up is a known effect in computational statistics.

Also, in situations where exp(-30) gives you roughly the relative accuracy of the double type, you would want to be extremely careful with accumulation of the round-off errors, as 1+exp(-30)=1: summing the likelihood contributions may run into numerical problems, especially when you start computing numerical derivatives and gradients. For a brief introduction into the issue in application to the typical problems in statistical computing and the specific problems it tends to encounter, see http://www.stata.com/meeting/nordic-and-baltic14/abstracts/materials/dk14_gould.pdf.