AirPlay Won't Connect Without Computer Restart

Hey guys,

I work at a school and all teachers have MacBook Airs from 2011 or newer, running 10.10.5 or newer. Many also have Apple TVs connected to projectors so they can use AirPlay to mirror their computers to the projectors. So here's the problem:

A couple of my teachers can connect to their Apple TVs and use them without issues, but when they disconnect from the Apple TV, the AirPlay image in the menu bar remains blue (which is normal when AirPlay is active). The problem is, the teachers can not reconnect to the Apple TV because the computer thinks it is still connected. We must restart the computer in order to connect again.

The computer will show the Apple TV as a device that we can connect to but it never connects once it has been disconnected. This is a problem because teachers often connect to show a video and then disconnect so they can work on their computers. So if they try to reconnect, they have to restart their MacBook Airs.

ATV is up to date. Has been restarted and connected to another network and still has the same issue. Not sure if this is ATV related or MacBook Air related. Both devices are connect to the same network which has no restrictions.