The way this works, apparently, is that the HI Frankfurt Airport North charges a flat fee of EUR6 for the shuttle from and back to the airport. The HIX Frankfurt Airport charges EUR5 per day, as stated on the website, but the definition of "day" is a period of 24 hours. So, if you arrive at the hotel in the afternoon or evening, and return to the airport the following morning, you will be within a "day" and only charged EUR5.