Once you've sync'd a Lodgix property to an Airbnb listing, that sync can only be turned off within Airbnb.
To unsync:
Login to your Airbnb account and navigate to the listings page or click on this link:
Select the Airbnb listing that needs to be disconnected from Lodgix.
Click the "Edit" button to edit the listing
A side menu will slide-out from the right, scroll down to Sync Settings
Select the "Disconnect" option:
Once you hit SAVE, the listing will be disconnected from Lodgix, a small confirmation will appear at the bottom of that interface. You will need to refresh the page to see that the Connected status has disappeared.
But wait, you are not done yet! That listing is still live on Airbnb, even if it's no longer connected to Lodgix. To remove or pause the listing completely, read on.
After the listing has been unlinked, you return to the listing page: https://www.airbnb.com/hosting/listings
More info on snooze, unlist or deactivate can be found here: https://www.airbnb.com/help/article/476/how-do-i-snooze-unlist-or-deactivate-my-listing
We've created a video that reviews both the process of unsyncing an individual listing, as well as disconnecting your entire account from Airbnb: