Since a while i’ve issues with Air-Play in combination with the Linksys E4200. i found across a forum post that the issue was caused by the WMM settings. Which is default on the Linksys software.
You have to go to Applications and Gaming > QoS
To solve my issue I had to disable the WMM Support settings > to Disabled.
After this change the Linksys E4200 didn’t reboot any more when starting Air-Play on an iphone ( this issue started after upgrading till 6.x can’t remember which one. )
I changed back to the default software after I got an upgrade of my ISP and the DD-WRT software couldn’t get the speed which I got from the ISP.