This is the most common reason a shipping discount "stops working": the customer used another discount that isn't allowed to combine with shipping discounts.
Both discounts must allow it
For a customer to get your shipping discount and another discount on the same order, both discounts must be set to combine:
Your shipping discount: under Combinations, tick Product discounts and/or Order discounts. Both are ticked by default.
The other discount: in Shopify admin, go to Discounts, open the discount, and under Combinations tick Shipping discounts.

If either side isn't ticked, Shopify applies only one of the two discounts.
The app's dashboard warns you when this is a problem: look for "Other discounts may need to be updated" and click Learn more to see which discounts need fixing.
Codes from other apps (Klaviyo, Facebook, loyalty, wholesale)
Discount codes created by other apps need the same setting. Many apps have a "combine with shipping discounts" option in their own settings. Check there, or ask that app's support.
Some, like older Klaviyo and Facebook codes, create discounts with no combine option at all. Our Discount Bridge app fixes this by turning on shipping combinations for those codes automatically, including existing ones.
Stopping free shipping when another discount is used
Untick Product discounts and Order discounts in your shipping discount's Combinations. Customers using another discount then pay normal shipping.
This only works if the free shipping comes from the app. A free rate set up in Shopify's shipping settings always shows. See My discount isn't showing at checkout.
Shipping discounts don't stack
Only one shipping discount can apply to a shipping rate. If a customer qualifies for several, Shopify picks the one that saves them the most. That's why there's no option to combine with other shipping discounts.
This is handy for tiers: create "$10 off shipping over $50" and "Free shipping over $100" as separate discounts, and customers over $100 automatically get the free one.
Thresholds after discounts
Combining controls whether both discounts apply. Whether a discount code affects your threshold is up to the condition you use:
Cart total counts the cart after product and order discounts.
Cart subtotal counts the cart before any discounts.