Around two weeks after the shipping deadine (not the day they marked it shipped, but the shipping deadline for the exchange) for domestic exchanges and around twenty days for international exchanges, you'll be able to click on the "Report No Gift Yet" button on the exchange status page. If it's been less than that, the button will be grayed out, so please be patient. You will receive a final notice email when you can mark the gift not received.
When confirming not received, please be sure to check the bottom box if you would like to be entered into the pool of potential rematch recipients.
If your Santa failed to mark a gift shipped, you will also need to report no gift at the same intervals as above.