Today for no apparently reason my Airplay button disappeared from iTunes. At first I thought it might be the router.. however after restarting the router and my computer the issue remained and oddly the airplay on my iPad and iPhone was working just fine.
A search on the web brought up a mentioning of IPv6 protocol on the network connection – sure enough, going into the Local Area Connection Properties (Control Panel > Network and Sharing Center) and unchecking the Internet Protocol Version 6, and then restarting iTunes caused Airplay to reappear… even stranger, going back in and re-enabling the IPv6 didn’t affect Airplay. So basically, it was just the toggling of the setting and restarting iTunes which fixed the issue…
Update 4/9: The airplay option disappeared again today and toggling the IPv6 brought it back…