What is the ruling on making a vow to allocate two specific days for reciting the Noble Quran, given that I understood that allocating a specific day for reciting the Quran is a religious innovation?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.

It is recommended for Muslims to recite the Noble Quran at all times.  It is disliked that one makes a vow to allocate two specific days a week for reciting the Noble Quran apart from other days of the week because he then has made a vow to neglect a recommended act. In such a case, it is recommended for him to offer an expiation like that of breaking an oath and recite the Quran on a daily basis to the best of his ability. However, if he makes a vow to recite the Quran on those two days without intending to abstain from reciting it on other days, then there is nothing wrong in that and he is required to fulfill his vow because, in this case, he has vowed to carry out an act of obedience to Allaah, the Exalted. Such specification is not considered forbidden because by means of that vow, the person is committing himself to recite the Noble Quran on those two days without intending to abstain from reciting it on other days. It should be noted that making a vow is disliked in principle. We would like to highlight that based on the first assumption, if the vow leads that person to forget what he had memorized of the Noble Quran, then it is incumbent on him to break such a vow, offer expiation like that of breaking an oath, and recite the Noble Quran on all days of the week so that he can review what he memorized of the Quran (and keep it fresh in his mind). This is because forgetting what one had memorized of the Quran out of negligence is considered a major sin by some scholars. Shaykhul-Islam Ibn Taymiyyah said:

"Forgetting the Quran after memorizing it is a sin. Ibn Hajar said in Fat-h Al-Bari, "The predecessors held different views about forgetting the Quran after having memorized it. Some considered it a major sin. Abu ‘Ubaydah narrated a mawqoof tradition on the authority of Adh-Dhahhak ibn Muzahim ; it reads, 'No one forgets what he had memorized of the Quran except due to a sin that he committed. Allaah, the Exalted, says (what means): {And whatever strikes you of disaster—it is for what your hands have earned, but He pardons much.} [Quran 42:30]'" [Al-Fataawa]

Forgetting what has been memorized of the Quran is one of the greatest disasters that can befall a person. Scholars also relied on the Marfoo‘ Hadeeth that was reported by Anas where the Prophet, sallallaahu ‘alayhi wa sallam, said, "The sins of my Ummah were shown to me and I did not find a sin greater than that of a person forgetting a Quranic chapter after having memorized it." [Abu Daawood and At-Tirmithi; its Isnad (chain of narrators) is somehow weak]

The same Hadeeth was reported through a Mursal Isnad with a slight difference in its wording: "…What a grave sin it is for the person to neglect what he had memorized of the Noble Quran!" [Ibn Abi Shaybah]

Furthermore, Abu Al-‘Aaliyah said: "We used to consider it as one of the gravest sins to neglect what one had memorized of the Noble Quran until he forgets it." [Mawqoof; good Isnad]

It was also reported on the authority of Ibn Seereen that he said, "They used to dislike the one who forgot the Quran and spoke against him in the strongest terms." [Saheeh Isnad]

Sa‘d ibn ‘Ubadah reported that the Prophet, sallallaahu ‘alayhi wa sallam, said: "No man recites the Quran and then forgets it, but that he will meet Allaah on the Day of Judgment maimed (or empty-handed, or with no excuse)." [Abu Daawood; its Isnad is weak]

This is the opinion of Abu Al-Makarim and Ar-Rooyani from among the Shaafi‘i scholars. They depended on the fact that neglecting to recite and review the Quran leads to forgetting it, which indicates that one does not take care of it and is negligent regarding it. 

Al-Qurtubi said:

"Whoever memorizes the Noble Quran or some of it has been placed in a higher rank than that of those who do not do so. If he fails to maintain such a rank of religious observance and allows himself to lose it, then he deserves to be punished for that. Neglecting to recite and review the Quran leads one to return to ignorance. Behold! Returning to ignorance after gaining knowledge is disastrous indeed."

Allaah Knows best.