What is the ruling on not fulfilling a vow to fast one day for each time one practices masturbation during a week, after stopping the fasting due to not remembering the number of unfasted days, and is it permissible to make up these days?

The questioner must repent sincerely from masturbation and resolve not to return to it.

Regarding the vowed fast that was not fulfilled without an excuse: - The Hanbalis held that it is obligatory to make up the fast along with an expiation for breaking an oath (kaffarat yamin). - The Malikis and Shafi'is held that it is obligatory to make up the fast without an expiation for breaking an oath. - The Hanafis held that it is obligatory to make up the fast, and an expiation for breaking an oath is required if he intended an oath with his vow. - Ibn Hazm held that there is no make-up or expiation for breaking an oath upon him unless he vowed to make it up.

The most accurate opinion is that only making up the fast is obligatory, without an expiation for breaking an oath. He must determine the days he missed and then fast all of them.