When your horse has been picked up as a match and a buyer opens a conversation, you won't miss it. The platform notifies you in two ways:
Email: You receive a message to the email address registered on your account.
Push notification: If you've downloaded the Floccs app and enabled "Allow notifications" on your phone, you'll get a notification directly on your screen and can reply immediately.
Once you reply, all your conversations are gathered in one place. See the guide: Where do I find my messages from buyers?.