That's my understanding of the language. It says it is valid for one day. To me, that means one full day, not a single visit, especially when coupled with the language that extends the validity to a second day if your journey contains overnight flights.

When I used day passes (and admittedly it's been perhaps 2-3 years), they never took them at the first club, they just stamped it and handed it back. Maybe they scanned it too. But they never kept it.