[One Fasting Two Consecutive Months in Expiation for Accidental Killing Eats by Mistake—Does He Resume Anew or Continue?]

Answer—and with Allah is success: What appears to me—and Allah knows best—is that the required consecutiveness has not been broken. The fasting person must withhold for the remainder of the day in which he ate by mistake or forgetfulness, it is not counted for him, and he continues fasting until he completes sixty days.
We say this for several reasons:
1- Allah the Exalted has lifted blame for mistakes, and its outward sense is general.
2- It is not within a responsible person’s capacity never to err or forget: “Allah does not charge a soul except [with that within] its capacity.” [al-Baqarah:286].
3- The questioner continued fasting the two months to the best of his ability: he refrained from food and drink on the day in which he broke his fast by mistake or forgetfulness, did not count that day, and continued fasting until he completed sixty days. This is what is within his capacity and power.
If it be said: He is able—in his power and capacity—to start over and fast two consecutive months anew,
It is said: Error and forgetfulness may recur each time he starts over, especially for one prone to forgetfulness. That would entail severe hardship if we were to say that he must start over each time he slips by error or forgetfulness. Yet Allah said: “And He has not placed upon you in the religion any hardship,” [al-Ḥajj:78] and “Allah intends for you ease and does not intend for you hardship.” [al-Baqarah:185].
If it be said: Fasting two consecutive months is a disciplinary fast with which Allah disciplined the unintentional killer and the one who declared ẓihār; hardship in it should not be found strange,
It is said: Even if it is a disciplinary fast, it is not made more stringent than Ramaḍān—except that no concession is given in it unless one fears harm if he fasts. As for error and forgetfulness, these are excuses from which it is impossible to be completely safe or to guard oneself altogether.
Source : Min Thimār al-ʿIlm wa al-Ḥikmah vol.1