Is there a limit for the number of discounts created?

Shopify imposes a limit for the number of discounts created by an app, as you can see at https://help.shopify.com/en/api/versioning/release-notes/2020-01#graphql-admin-api-changes

However, this limit is quite generous (20,000,000 discounts at this moment) so it shouldn't be a problem for most stores.