Is it obligatory to pay the full monthly subscription fee to the Qur'an memorization center, given that the children were absent for an entire month and did not attend their classes?

The answer to this depends on the type of contract (subscription). If it is a monthly contract without a specified duration, then it is not binding on either party. In this case, the questioner is not obligated to pay the fee for the month her children were completely absent. However, for a month in which they attended even for a single day, she is obligated to pay the full fee for that month.

However, if the contract is for a specified duration, such as a full year or a complete academic semester, then the questioner is obligated to pay the fee every month, whether her children attend or not, for the entire duration of the contract.