I don't know why the bus doesn't show, but if you've used the same format as about (MM-DD-YYYY) then it doesn't work - you have to use DD-MM-YYYY.
When I look on Midttrafik’s website for route 925X (Aarhus Airport bus), there does seem to be a bus for SK1244 on 25 August, 2026. It does however also appear that it arrives at 09:40, which seems to also be the departure time for the flight. Do I have that right? If that’s the case, then it obviously doesn’t work.
Might be a good idea to reach out to Midttrafik and inquire about it.
EDIT - The arrival time confusion may be that I'm currently in another timezone. When looking at Rejseplanen, it appears to arrive 08:40. I encourage you to double check, of course, but here's a link to what I found.