Improper form. An example that quickly comes to mind is the practice of “sprinkling” babies. This isn’t a true baptism for several reasons: (a) the baby isn’t repenting nor consenting because (b) the baby hasn’t any awareness of sin. It (c) hasn’t reached a responsible age of spiritual awakening nor (d) has it been reborn. And (e) “sprinkling” doesn’t follow the biblical model of the early Christians.
The Greek word for baptism is “baptizo.” It means to dip under, submerge, or immerse. Baptism is symbolic of the death and burial of the old life of sin. Jesus modeled for us the proper method. It was voluntary, full water immersion. In this way, Jesus said, all righteousness is fulfilled. So if one’s first “baptism” didn’t follow suit, it wasn’t a true baptism. That, then, would be legitimate grounds for being re-baptized.
Greater light of truth. Even if the first baptism is legit, it is okay to be re-baptized if one subscribes to a new Bible teaching that is of a life changing nature. For instance, one may discover that current beliefs, though sincere, are violating some very important principle(s) of scripture. Or one may learn of biblical teachings that alter or transform the worship of God.
Under such circumstances, if one feels the need to re-baptize, he or she would be in good company. I’m thinking of the Ephesian believers that the apostle Paul taught in Acts 19: 1-5. After learning about the Holy Spirit – though they had already been baptized by John the Baptist – they requested and were re-baptized by Paul in the name of Jesus.
Coming back to the faith. Symbolically, baptism is also akin to getting married. It is a public vow to be wedded as the bride of Christ. So when one breaks up with Jesus, reverting to the former life of sin, it is the same as being divorced.
That one has returned to Jesus certainly warrants being re-baptized.