Repentance doesn't earn salvation, repentance is the means by which we accept salvation - through exercise of free will choice, plain and simple.
When Christians realize that choice is not "work" but is merely "thought", then they will cease from this confusion of a false dichotomy between faith and works. Thus, works have nothing to do with obtaining salvation, they are the evidence that salvation has been obtain - through repentance- and that is why the absence of works is evidence to the contrary.
1 John 2:3-4 KJV says it all. The problem is our love of sin refuses to allow us to accept what is written here, but if we look to the Cross and see what sin has done to Jesus, God will grant us a hatred of it...which is all He ever wanted for us to have.
Repentence is also how you show God through your choices and actions that you are sincere about turning away from a sin.
Note this is not the same thing as struggling with a sin like an addiction.
For example, I repent of murder, but... continue murdering. On purpose. That's not repentance. That's just a cover and excuse.
But let's say I have an addiction to it. Well. If you can't stop it, and it's something with such serious consequences, turn yourself in and beg for mental help at least.
Scenario 2, one is at least trying to turn from the sin.
Mind you, I only use that particular sin as a blatant example.
Littler sins can include things like alcoholism and the things one might do when drunk.
But one should still be seeking out help for a sin if one has trouble with it. But it's the difference between a sincere effort and using forgiveness as a license to sin.
To the adultress, Jesus forgave her, but He did give her a command: "Go and sin no more."
He forgave her, but He also told her to stop doing it.
True repentance is not just feeling bad but making the effort to stop doing it and to CHANGE.
Repentance is an action and choice, not a feeling.