That’s an interesting question.
I presume you refer to new arguments against Catholic doctrine, and not new arguments in favor of their own beliefs.
The Early Fathers wrote both dogmatically (Against Heresies) and pastorally (Ten Homilies on John). Most writings are pastoral. We sometimes find protestant ideas refuted in pastoral writings, even though the original intent was not to refute anything. For example, modern Baptists (despite the irony of their name) believe that Baptism is a mere symbolic ceremony to commemorate a salvation event that has already taken place. Nobody in the early age of the Church ever had such an idea (there were many debates about Baptism, but nobody claimed it did nothing), so nobody back then made any deliberate attempt to refute it, but we have lots of pastoral writings that support the Catholic position that we can turn to in modern times. The same could be said for Eucharist and many other things.
But have protestants managed to come up with something completely original that nobody in the early Church had ever given a thought to? I gotta think about that.