After considerable research I have concluded that this is a long standing issue with airplay that to this day has not been fixed.
I have sling player installed on my macbook pro and have no issues with airplay.
Switch to my iPad or my iPhone 6 and try to airplay and its an exercise in frustration.
Often I get an error message saying it won't connect. The best work around seems to be start airplay before I start streaming the sling player. This however is not full proof. More tinkering is often required. Switching the mirror function on/off seems to stabilize the stream.
I hate having to use the mirror function in airplay because it changes the aspect ratio of playback and you end up with black boarders on your TV.
Checking out some reviews on this app and I realize I'm not alone. https://mixrank.com/appstore/apps/405564910/reviews?sort=rating-asc&page_size=50&offset=10
This forum is also littered with people complaining of the same problem, with no real acknowledgement or fixes from support.
Hop over to apples support community and you will find the same thing.