When deleting the application did you delete the App from your personal page, your business page or both? Make sure when deleting the app that you are logged in as yourself (your personal account that is an admin on the business page). I just went into a test business page that I have on Facebook and was able to go to the Settings on the Page, then to Apps and click the "x" to delete the app and it was removed immediately, see the screenshot below. (I am using the new/updated view for business pages, in case this looks unfamiliar. To get to the App Settings in the old layout you can click Edit Page > Edit Settings > Apps)
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