The Delivery Limit Date is based on your delivery's validity settings. This can be found in your delivery Properties section within the Validity tab.
See below as an example:
The delivery date error that you are getting is based on the "Length of Delivery" setting. This means that after the contact date, the delivery will continue to send for X number of days (in this case 1 day). After which any further attempts to send will fail with the error that you are seeing.
This setting only applies to sending, it does not apply to tracking, so any recipients that have received the delivery can still have opens and clicks register even after the Length of Delivery has passed.