I'm not sure I fully understand how to replicate the issue. Can you provide a bit more details on exactly what I should search for ? As when I tried the texts in your initial posts i'm not seeing any duplicates.
By default, results are sorted by rating (field-mrp_rating_result_1_star_rating), and then I try to automatically sort by event date, when user searches for current events (input #in-faktor-806 / Aktuelle Veranstaltungen) is activated.
I'm doing that by jQuery on a hidden part of the search form:
E.g. when search for "Fächer -> Mathematik (Kern)" is initiated from homepage (hidden link), sorting will be messed up ("Quadratische Funktionen erkunden" will be on top,
in the first 5 places items 27-31 will be displayed, and these will be repeated in their right places.
(The first 5 DISPLAYED items will always be a block of 5 items from further down the results list, and these will be REPEATED in their right places.
The more items are found, the further down in the search results is that block the first 5 DISPLAYED items will be taken from.)
Then after deactivating and again activating that "Mathematik"-Tag, sorting will be ok again! ("Mathefragen" will be on top.)