Question: Can a card issuer design the minimum amount due so unpaid fees keep getting capitalized into interest?
Answer: No. Credit-card payment terms, including minimum amount due, must be structured to avoid negative amortization, and unpaid charges, levies, or taxes must not be capitalized for charging or compounding interest.

Supporting evidence:
title: rbi.org.in/BS_ViewMasDirections.aspx
quote: The terms and conditions for payment of credit card dues, including the minimum amount due, shall be stipulated so as to ensure there is no negative amortization The unpaid charges/levies/taxes shall not be capitalized for charging/compounding of interest
context: R shall be given with clear examples for better comprehension. The APR charged, and the annual fee shall be shown with equal prominence. The late payment charges, including the method of calculation of such charges and the number of days, shall be prominently indicated. The manner in which the outstanding unpaid amount has been arrived at for calculation of interest shall also be specifically shown with prominence in all the billing statements. These aspects shall also be shown in the Welcome Kit in addition to being shown in the billing statements. ii.

The terms and conditions for payment of credit card dues, including the minimum amount due, shall be stipulated so as to ensure there is no negative amortization. An illustration is included in the Annex . The unpaid charges/levies/taxes shall not be capitalized for charging/compounding of interest. iii. iv Card-issuers shall inform the cardholders of the implications of paying only 'the minimum amount due'. A legend / warning to the effect that "Making only the minimum payment every month would result in the repayment stretching over months / years with consequential compounded interest payment on your outstanding balance" shall be prominently displayed in all the billing statements to caution the cardholders about the pitfalls in paying only the minimum amount due. The MITC shall specifically explain that the 'interest-free credit period' is suspended if any balance of the previous month's bill is outstanding. iv. For this purpose, card-issuers shall work out illustrative examples and include the same in the Welcome Kit sent to the cardholders and also place it on their website. v. v Card-issuers shall report a credit card account as 'past due' to credit information companies (CICs) or levy penal charges, viz. late payment charges and other related charges, if any, only when a credit card account remains 'past due' for more than three days. The number of 'days past due' and late payment charges shall, however, be computed from the payment due date mentioned in the credit card statement, as specified under the regulatory instructions on 'Prudential norms on Income Recognition, Asset Classification and Provisioning pertaining to Advances' amended from time to time. Late payment charges and other related charges shall be levied, only on the outstanding amount after the due date, and not on the total amount due. vi. vi Interest shall be levied only on the outstanding amount, adjusted for payments/refunds/rev