This is a question that comes up repeatedly. Some of the reasons given are as follows:
- The person did not understand Jesus' sacrifice on the cross.
- The person was confused as to what he/she would receive at baptism: forgiveness of sins and the Holy Spirit.
- The person "held back" something (either through not confessing sin or not wanting to change from a particular sin) and/or didn't make Jesus Lord of his/her life 100%.
- The person got baptized to please people, such as family members or friends, or did it to find acceptance from the church.
- The person did not have a clear conscience before baptism, i.e., felt "wrong" after getting out of the water or had bad thoughts right after.
- The person's life after baptism (usually from observation of 1-2 years or so) does not appear to reflect the life of a disciple.
- The person did not repent before baptism.
So, are there circumstances under which someone should be baptized again? Since our appreciation of Christ continues to grow the longer we follow him, repeat baptism for (1), (3), (4), (5), and even in some cases (6) lacks biblical precedent. Besides, knowing one's motives is a tricky business (1 Corinthians 4:4-5). Probably most of us come to baptism with several motives.
As for case (2), understanding the purpose is a logical inference from scripture. Of course we want people to understand why baptism is so vital, though there is no slam-dunk passage proving that perfect understanding is essential to salvation. Ultimately, these cases generally boil down to a personal decision. This is difficult to frame as an absolute, salvation-related issue.
Now when I meet someone who appears to be living as a disciple yet may have a slightly different understanding of how God's Spirit works, I nearly always ask about (7). If that person repented before baptism, I usually let it go. I trust God that his/her developing understanding may lead to some serious rethinking at some future point. But when the believer did not intend to make Jesus Lord at the moment of conversion, I cannot in good conscience welcome that person as a brother/sister in Christ.
For further study, please start with some searches here on the site (e.g., "John's baptism," "confession," "re-baptized"). For a more in-depth exploration, please take a peek at my book, The Spirit.