If you watch this video on YouTube
starting at about 3:25, you will see the player not get the keys successfully and then see him get the keys successfully on the second try.
I don't have much else to offer for this - I remember folks posting about this in the past, people who had been trying for days to get the keys and were not able to manage it. I don't know if this is a time problem, or whether you have to be clicking in exactly the right spot on the staircase or what, but it seems to be problematic for a lot of people.
I also found this old thread on GameBoomers here.
It seems you had this problem last year - were you able to get past it then?