For the most part, when you purchase an app, it's your forever. There are apps where you purchase a service which is recurring. For example, Mantano Reader has a premium version which once you buy will always be yours. It also offers an optional service to store your books in the cloud and sync them between devices. This costs a few dollars a year. Mantano Reader will be yours even if you delete it from your device or decide to install on another device but the sync service is recurring (if you choose to use it).
I hope I didn't confuse you and make things worse.