How many data needed for mnrfit?

For example an N = 10 dimensional problem with K = 10 categories and M = 1000 test data the mnrfit algorithm is executed for me without convergence warnings. But increasing N or K a little bit, for example to 15, I always get warning messages for M = 10000 or M = 100000 data points also. Is it possible? Are there any practical rule for estimating the necessary data points?