Is repeated repentance for the same sin accepted after repeatedly committing it, and is an expiation for an oath (kaffarat yameen) incumbent upon one who breaks their promise not to return to the sin?

Allah continues to accept the repentance of a servant as long as they turn to Him in repentance. So, beware of despairing of Allah's mercy. No matter how many times you commit a sin, repent whenever you sin and do not grow weary. No matter how great your sin, Allah's forgiveness is greater. Ibn Al-Qayyim said: "Indeed, Allah forgives His servant as long as they repent every time they sin." This ruling applies to everyone whose condition is such. The statement you made is not considered an oath or a vow, and nothing is binding upon you because of it.