You can repent as many times as you can be truly sorry about the sinning that got you to the place of needing to repent. But anytime you would not be truly sorry would not count as true repentance. And going back to the same sin would be proof of that.
Let's say a woman has a husband who has been unfaithful. Then he comes and apologizes and says he is truly sorry and his wife forgives him. Is it a right mindset for that man to ask his wife how many more times he could cheat on her again and "repent" to get back again like everything is good? I don't think so. Even if that wife has a big heart and would find it in her to forgive that man even many times, something is not right in the marriage/relationship between these two people. Especially, the conduct of that man shows that his heart is not on loving his wife and protecting his marriage and family at all cost. He is double-minded. It's like he regrets getting married.
So, when we come to Jesus, it's like we get married to Him spiritually. And He expects our faithfulness to Him as much as we can expect his faithfulness to us. It's all out of love. This is the way we are called to approach God:
James 4:7-8
7 Submit yourselves therefore to God. Resist the devil and he will flee from you. 8 Draw near to God, and He will draw near to you. Cleanse your hands, you sinners, and purify your hearts, you double-minded.
We can't be double-minded about agreeing in our heart to live our life in submission to God, to no longer seek pleasure in any deliberate sins (knowing right from wrong and still keeping on choosing to do wrong). When we turn to God, we leave behind any mindset that we can get close to God while still continuing to sin, because sin itself is what keeps us separated from God (cf. Isaiah 59:2). A life ruled by sin is what Jesus saves us from, so life as a Christian (follower of Jesus) is not a cycle of going on sinning and repenting.
The idea that sin goes on and on in Christ is not from the Bible.
Matthew 1:21
She will bear a son, and you shall call his name Jesus, for he will save his people from their sins.
Acts 3:26
To you first, God, having raised up His Servant Jesus, sent Him to bless you, in turning away every one of you from your iniquities.
2 Timothy 2:19
Nevertheless the solid foundation of God stands, having this seal: “The Lord knows those who are His,” and, "Let everyone who names the name of Christ depart from unrighteousness."
1 Peter 4:1
1 Since therefore Christ has suffered for us in the flesh, arm yourselves likewise with the same mind: for he who has suffered in the flesh has ceased from sin; 2 That he no longer should live the rest of his time in the flesh to the lusts [desires] of men, but to the will of God.
Romans 6:4-7
4 We were buried therefore with him through baptism to death, that just like Christ was raised from the dead through the glory of the Father, so we also might walk in newness of life. 5 For if we have become united with him in the likeness of his death, we will also be part of his resurrection; 6 knowing this, that our old self was crucified with him, that the body of sin might be done away with, so that we would no longer be in bondage to sin. 7 For he who has died has been freed from sin.
See also:
Is Repentance Just a Change of Mind?
Past Sins are Forgiven — Past, Present and Future Sins are NOT Pre-Forgiven
Sinning Willfully and Sinning Repetitively
Jesus came to save sinners from sin (Matthew 1:21)
