Question

I was afraid if I asked him again he.... Refuse (can, may, might)

Answer 1

might is the word in the blank

Answer 2

I was afraid that if I asked him again, he might refuse.

Explanation:

Modal Auxiliary verbs describe the modality of the situation like possibilities, ability, likelihood, probability, etc. It usually escorts with another form of a verb. It can also be used to form questions.

Some examples of modal auxiliary verbs are might, may, could, will, etc.  The above sentence explains the possibility of an event. Therefore, a model auxiliary verb is used to describe the likelihood of the situation.