Managing a Promotion Free Delivery

If you have a promotion that has free delivery associated to it, then there should be a discount added for each service level available - 

Then, providing each specified service level has an associated delivery option on a Delivery Zone, the discount will fire -

As you can see, the promotion Delivery Discount does not have a service level option for Named Day Delivery or Named Saturday Delivery - meaning that if a customer were to have an order placed using one of those options, then they would not get any delivery discount from that promotion. To resolve this, the delivery discount should be added for that service level -