Should the apportionment towards exempt supplies/ non-business purposed be done only on a monthly basis

No. The recipient is required to do the apportionment on an annual basis also before the due date of filing the return of the September month of the following year. The differentials will be liable to be paid with interest (if the annual disallowance is higher) and will be eligible as credit (if the annual disallowance is lesser).

(ICAI FAQ PUBLICATIONS 06-09-2017 INPUT TAX CREDIT : FAQ NO. 59)