I recently tried to buy Office 365 from MS India. It just kept on failing with my India debit card even though it accepts both debit/credit cards. The error message was not helpful and finally came to know from customer care that it was due to the debit card. So, it can go both ways.

Recurring payments have been intentionally blocked by the banking regulator in India by requiring 2FA for every online transaction to prevent abuse/fraud. It is a known pain intentionally traded off - hopefully will get fixed at some point.

I think the issue with international cards is also likely linked to online transaction 2FA policy. Some American banks don't implement 2FA and that's likely the reason they fail. I've never had a problem with my Singapore card.