In many existing systems, there's a split between "merchant" and "customer" cards, of which only merchant cards are allowed to accept payments. Merchants often have to go online once per day and batch-submit all of the day's payments in order to be guaranteed settlement.
Among other advantages, this allows for a "lost/stolen" card feature: If a user loses a card, that card can be denylisted on a global list synchronized to all merchant terminals daily. After another day of waiting for straggler transactions, it's possible to determine the remaining balance of the lost card from the backend, and reimburse its owner, since further funds on the card can no longer be spent anywhere in the system.
One day is essentially just an arbitrary timespan here – you could make it 14 days, or an hour. In the systems I've looked at closely, one day makes sense because these are historically transit-focused, and e.g. buses don't have continuous network connectivity, but do go to a depot in the evening, which is a good opportunity to clear and settle all of the day's payments.
Customer cards never need to be online in such a scheme.