In many cases, you'd write verb + gerund:
His eyes stopped to sting/stinging after a while.
What is it an exception with the verbs struggle and process?
He struggled to process/processing the news.
English Language Learners Stack Exchange is a question and answer site for speakers of other languages learning English. It only takes a minute to sign up.Sign up to join this community
From this source:
A transitive verb is a verb that requires an object to receive the action.
An intransitive verb does not take an object. Using an object immediately after an intransitive verb will create an incorrect sentence. However, there may be other information after the verb, such as one or more prepositional phrases or an adverb.
So in your first example, the gerund
stinging is the noun receiving the stop action. Whereas in the second example, struggle cannot (grammatically, at least) take an object, so you achieve that goal with the infinitive instead.