A present stem verb form, here the present participle, can have either a specific or general interpretation. If it is specific, it would mean that the seeing or believing is on-going when the person has eternal life. If it is general, then it could refer to something that is habitual and so it is only necessary that seeing and believe is a characteristic part of the person's behavior. Just as other habits permit the occasional exception, I don't see anything in the general / habitual interpretation of the present stem that necessarily requires persistence or consistency of seeing and believing, though it does not exclude it either.
As for the fifth point of Calvinism, please note that this forum is for discussing the Greek text, not systematic theology. In fact, theological discussions are considered out of bounds here.
Stephen C. Carlson, Ph.D. (Duke)
Post-Doctoral Fellow, Faculty of Theology, Uppsala