The truth of faith cannot be definitively proved by any rational argument. The fact constitutes the believer's predicament. Hence the old rule of thumb: "The Christian who wishes to conduct a disputation on his belief should not attempt to prove his belief but to defend it."
This is a good rule to keep in mind. We don't want to exaggerate what can be proven, or we'll lose credibility when we fail to prove our belief -- and what can be proven, in any case, isn't a belief.
At the same time, we shouldn't feel defensive about defending our faith, as though if we were smarter we'd have irresistable arguments. Being ready to give an explanation to anyone who asks us for a reason for our hope is what we're asked to do, not give a reason for why everything else is demonstrably unreasonable.
And, as Pieper points out, this is true of internal disputations as well. There may be times when the only way to defend your faith against your own arguments against it takes "the form of silent defenselessness, as in the case of the martyr."