My name is Kris and I'm a guru, here to lend a hand. :)
Your customers should definitely have the ability to be offered a free shipping rate (pulled from your Shipping settings), while still having the function to redeem your discount codes. I performed a quick test to validate this and you can see an example from my test store's checkout here.
One factor that may come into play is if the discount itself is reducing the price of your customer's cart, where they no longer in fact qualify for your price-based free shipping rate. For example, if free shipping is set up for orders over $50, but the discount code makes the order cost less than this amount, their purchase would no longer meet the requirements and their shipping rates will be adjusted.
If you have suspicions this may be happening for another reason I would encourage you to reach out on our Support Channels, so it can be looked at in more detail.
|an hour ago|