Second presentment is another name for chargeback representment, the step in which a merchant, through its acquirer, rejects a chargeback and sends the transaction back to the card issuer with supporting evidence. The main entry explains how representment works and what evidence is used. The term is used mainly in Mastercard's dispute rules, while Visa's process refers to a dispute response.
The name reflects how card transactions are cleared. The original sale is the first presentment, when the acquirer presents the transaction to the issuer for payment. When the issuer raises a first chargeback, the acquirer may present the transaction a second time, now with documents such as delivery proof, signed terms or proof of a refund, arguing that the chargeback is invalid.
If the issuer accepts the second presentment, the funds are returned to the merchant. If not, the issuer can continue to pre-arbitration and, eventually, arbitration by the network. Each stage has strict deadlines set by the scheme, covered in the entry on the chargeback lifecycle.