EDIT: Having re-read your question, I realized that the "any case" doesn't seem refer to the two reasons, but rather to some other (yet undiscovered) set of instances or circumstances. So I'd go with "any" in this case since the number of such "cases" is undefined.
ORIGINAL: Both are fine, but if there were more choices offered, "any" would be the choice, since "either" indicates exactly two choices. In this context, "any" will also have the effect of preemptively including any other options offered by your interlocutor.