If one repents & sins again, is further repentance accepted?

G-d does not view a person as a “nuisance” for repeatedly asking for forgiveness.

The patience of a human being will eventually wear thin if he is approached with requests for forgiveness many times, but G-d’s patience has no limitations. His patience for those who sincerely turn to Him is infinite. (Although His patience in waiting to be asked for forgiveness is limited to the length of the person’s physical life!) A person should strive to be a “master of accounts,” setting aside some time on a regular basis to review his thoughts, speech and actions, to recall what was not proper and what needs repenting for. (This is especially important during the month of Elul, which is the month before G-d’s annual day of judgment on Rosh HaShanah.) But a person’s self-evaluation needs to be done in a positive way, and not in a way that would lead one to fall into depression, G-d forbid, since that is one of the tricks employed by the evil inclination.

A person should have absolute faith that when he approaches G-d in proper repentance, G-d accepts it – even if the sin was repeated many times. On the other hand, one should not then put the sin that he did totally out of his mind from then on. As King David said in Psalm 51, “… my sin is always before me.” The person will thus remain humble before others no matter what spiritual level they are on, even though he himself is now advancing spiritually way beyond his former level. Also since the person has that weakness, his vigilance should be maintained. And it may be that G-d desires for the person to reach for more sincere levels of repentance than he has achieved until now.

But this is only one aspect of a person’s relationship with G-d, and it should be given full attention only at designated propitious times. The main aspect of a Noahide’s relationship with G-d throughout most of the day should be with joy at the opportunity one is graciously given by G-d to serve Him (and connect with Him) through making the world a better place by observing and promoting the Seven Noahide Commandments.