There is no specified limit to the number of discount codes that can be added to a discount set over time, however you are limited based on the type of discount set being created.
For generated discount sets, there's no limit to how many codes you can generate at a time. There may be unknown limits to the number of discount codes allowed in Shopify, however.
For specific code discount sets, there's a limit of 10,000 codes per import. Once a discount set of this type is done importing, you may add additional codes in increments of 10,000.