This was a tough question. Repentence is absolutely required for salvation. But I think many misunderstand what repentence is. Repentence is to turn from unbelief, to turn from trusting in one's own righteousness and trust Christ alone for salvation.
Mark 1:15 And saying, The time is fulfilled, and the kingdom of God is at hand: repent ye, and believe the gospel.
So, repent means to turn from unbelief.
Are we supposed to turn from sin once we accept Christ? Absolutely, it is said many times in the scriptures.
2 Tim 2:19 Nevertheless the foundation of God standeth sure, having this seal, The Lord knoweth them that are his. And, Let every one that nameth the name of Christ depart from iniquity.
Now, the way I see it, if you truly and sincerely believe Jesus is the Son of God, you are going to listen to him. And it is clear that He wants us to live as good and holy life as possible.
I believe in Preservation of the Saints. We do not save ourselves, Jesus does, and we cannot keep ourselves, Jesus does. When a Christian sins he does not lose his salvation, but he does lose rewards.
1 Cor 3:15 If any man's work shall be burned, he shall suffer loss: but he himself shall be saved; yet so as by fire.