~Finally~, Reeder for iOS has updated to v2.2, now with background app refresh and a load of other awesome features and fixes. Go get it.
Minor tangent: As much as I enjoy using Jared Sinclair's unique RSS app Unread, I always come back to Reeder. It has a slow development cycle to be sure, but after all these years I still love its sheer speed and simple design. Unless Silvio Rizzi goes out of business, I can't see myself ever needing another RSS app.