What should one do who repeatedly falls into a specific sin, regretting it each time; is that considered a breach of the covenant with God?

The means of ridding oneself of sin, after Allah's help, is through striving [against one's lower self], enduring hardships, self-accounting, and restraining the soul to obedience. Whenever you fall into sin, promptly cease it and renew your repentance. Do not despair of Allah's guidance. And before all of that, you must supplicate and humble yourself before Allah. The Prophet, peace and blessings be upon him, said: "Every son of Adam commits sins, and the best of those who commit sins are those who repent." So, it is not a disgrace to err, but the disgrace is to err and not repent. Even if the sin is repeated a hundred times or a thousand times, and one repents each time, their repentance will be accepted.