A stamp is written immediately at Goodly; what appears on the phone then depends on the Wallet.
On iPhone
Apple Wallet requests the new version of the card after a signal from Goodly. It needs a network connection and the "Automatic Updates" option enabled in the card details ("⋯" button, then on the back of the card). If the card stays frozen, ask the customer to open the card, then pull it down to force a refresh.
On Android
Google Wallet updates when the customer opens their card. Check that the phone is connected.
From the dashboard
Save the card again in My cards → Customize: each save sends the card back to all Wallets. The "Notify customers" button adds a notification. The counter shown corresponds to requests accepted by Apple or Google, not to proof of delivery.
If only one customer is affected, check in My customers that you stamped the right card (a customer can have several cards or several businesses).