To universalize a suicide maxim is to take it as a law of nature; nature already has a law that we strive, even amidst adversity to live; hence, a contradiction would exist between a law driving our survival and a law driving our suicide... "One sees at once a contradiction in a system of nature whose law would destroy life by means of the very same feeling that acts so as to stimulate the furtherance of life, and hence there could be no existence as a system of nature. Therefore, such a maxim cannot possibly hold as a universal law of nature and is, consequently, wholly opposed to the supreme principle of all duty."
That, at least, is the canonical formulation.