> Your card limit gets checked on every transaction.
Nope. The merchant can choose the level of verification - in some cases, like copying the card with an imprinter [1] or running phone transactions (yes, that is possible - it's called MOTO [2]), it's obviously impossible to check card limits.
Downside of CNP transactions is, the merchant is fully liable for anything from fraud over chargebacks to exceeding limits.
And then you got card-present transactions but the network connectivity is down for whatever reasons... been a while since I messed with that, but at least for German cards you could configure the terminal to store the account details for later submission when connectivity was restored.
[1] https://en.wikipedia.org/wiki/Credit_card_imprinter
[2] https://docs.adyen.com/point-of-sale/mail-and-telephone-orde...