Airplay code menu entry box disappears before code can be entered.

Hi this question has been asked before but there was no reasonable answer given.

The gist of this is that concerns attempting to connect to Apple TV from iMac and I tunes on my apple desk top computer. Whilst I have the system on an ethernet and the computer is up some stairs in my home (first floor) by the time the Air play menu box appears on the iMac and I then run down stairs (only one flight) I then go through a small hall way and in to a lounge to the read Airplay code off the Apple TV screen and I then run back upstairs, by the time I get there the Airplay code menu box has closed down / disappeared of its accord. Someone else had the same problem and the answer given revolved around that first person possibly using WIFi and a distance issue. But WIFI is NOT being used in my case. Q. Is there a way to extend the time the I tunes Airplay code enter box stays avaialble and open to give enough time to collect the requested Airplay Code from another room and then return to enter it on my iMac which is on the first floor of a single story house in the U.K? The time display needs extending please how do I do this?