Contraposition is not valid in the case of which categorical proposition?

Contraposition fails for the particular affirmative proposition, 'Some S is P'.

Contraposition proceeds by obversion, then conversion, then obversion, so it depends on a legitimate conversion in the middle.

The particular affirmative obverts into a particular negative, and a particular negative cannot be converted validly.

Hence no equivalent contrapositive can be formed from 'Some S is P'.

The particular affirmative is therefore the one categorical form with no valid contraposition.