A person can get wet on top of the head, all over, once or repeatedly and it isn't necessarily baptism. Otherwise, every person who has ever taken a bath would be baptized, and no one claims this to be the case. So, what makes baptism, baptism? I suggest that it is not our human activity at all, but what God does. The primary actor in baptism is neither the individual being baptized nor the person officiating, but God and God alone. Thus, baptism is not about the individual who confesses faith and declares his/her relationship with God, but God's declaration of his relationship with us. And that relationship is one of grace even more than it is one of faith, for there is grace that comes before faith and leads us into faith. And that prevenient grace, expressed by Christ's death and resurrection which occurred "while we were yet sinners" (Romans 5:8), is what we are celebrating in baptism. That an adult believer may claim it is indeed worthy of being celebrated, but it is no less true and present in the lives of infants for whom the church itself makes a declaration of faith.
So, the validity of baptism is vested not in the person, nor even the act itself, but in God. Now, the only reason that certain denominations practice what some people call re-baptism, is because they do not recognize the validity of a previous baptism. Hence, those denominations are saying that there was no first baptism. And if there was no first baptism, then there can be no re-baptism. But, if the original baptism was valid, as I claim, then there is no need for a second baptism. God does not confer any new or additional grace upon a person as if he held back his grace in the first instance. No, all the grace that God has to show is already present in this individual's life. Thus, any attempt at a "re-baptism" is a very human act, not a divine act. And therefore it isn't truly baptism, for the person was already baptized, an unrepeatable act.
So, what of the person, baptized as an infant who grows up apart from the church and comes to faith later as an adult and wishes to celebrate their new found faith? By all mean, celebrate it. You may even wish to have a celebration with immersion water and a confession of personal faith in which one re-creates or remembers one's baptism. But it isn't baptism, nor re-baptism.
Over the years as a pastor, I have been asked to perform a number of weddings. And a few instances where people who were already married renewed their vows. Now, imagine this situation. A couple get married when very young. They really don't have any idea what they are doing, and the relationship goes sour very quickly. Soon they are separated and each go their own way. But they are young, and don't have any children nor property, so they don't even bother to file for a divorce. The years pass, perhaps they are in and out of other relationships, but none of them last either. And then one day when they have finally grown up, they happen to meet again. They begin to date. A bit more slowly this time, but soon a full-fledged romance blossoms, and this time they determine that they really do want to commit to one another. What should they do? Do they get married? Remember, they are already married. Do they get remarried? You can't get remarried until the first marriage has ended, and they are in fact still married to each other. It would no doubt be entirely appropriate for them to renew their vows, but there would be no filing of a marriage certificate, nor recording of a marriage as having taken place. For in fact they are not getting married. They are affirming and finally getting around to committing to a marriage that has been valid all this time, even if not lived out.
And baptism, one in which God is truly present and commits to us is valid and long-lasting. Having baptized us, we cannot be re-baptized for God does not break his covenants and need to redo them. Even if we are faithless, he is faithful and never removes his grace actions from our lives.