We are having problems with some orders that are going to cancelled, even when we have payment on our payment system. Can anyone help?
It depends on what your payment method was and how the order was cancelled. If your payment was set to authorize only, then when you cancel the order it won't capture it.
If your payment method was set to authorize and capture then it will depend on your payment integration hat happens when an order is cancelled if it will also trigger a refund for the transaction.
Even if does trigger a refund for the transaction, the gateway might not be able to refund the transaction until the batch settles.