This is something of a strawman, but suppose one of your deontological rules was "thou shalt not kill" and you refused to accept outcomes where there is a positive probability that you will end up killing someone. (We'll ignore the question of how you decide between outcomes both of which involve killing someone.) In the notation of the Wikipedia article, if L is an outcome that involves killing someone and M and N are not, then the continuity axiom is not satisfied for (L, M, N).

Behaving in this way is more or less equivalent to having a utility function in which killing people has infinite negative utility, but this isn't a case covered by the VNM theorem (and is a terrible idea in practice because it leaves you indifferent between any two outcomes that involve killing people).