If a customer's card payment fails halfway through checkout, does their money get stuck somewhere?

No, in almost every case the money comes back to the customer on its own, but it can sit in limbo for a few days first and it helps to know why.

When someone pays on your website, the bank first puts a hold on the amount rather than handing it straight over. If the payment then fails, or the page drops out before the booking is finished, that hold is never turned into a real charge. The customer often still sees the amount missing from their available balance, which is why they ring you in a panic, but their bank releases it by itself after a few working days. Nothing has reached you, so there is nothing for you to refund.

On your side the booking is not confirmed and is kept as a failed or incomplete attempt rather than being thrown away. Your staff can see it, see the reason the payment provider gave, and either send the customer a fresh payment link or ask them to try again. That record matters, because it lets you tell a worried customer exactly what happened instead of guessing.

The part that is out of everyone's hands is timing. How quickly the hold disappears depends on the customer's own bank, and no software can speed that up. It is also worth remembering that a failed payment does not hold the seat or the room, so the price may have moved by the time they try again. If a customer calls about this, check the payment status on the booking first, then ask them to look at their statement rather than their available balance.