Welcome, AppleTVcutsout!
Thanks for using Apple Support Communities! From your post, it sounds like our Apple TV is disconnecting while watching a movie. We want to help find a solution with you.
Is your Apple TV disconnecting from Wi-Fi, causing your movie to pause, or is it disconnecting from your projector?
If it disconnects from Wi-Fi, we want to see if the troubleshooting steps in the following support article will help resolve this:
If your Apple TV won't connect to Wi-Fi - Apple Support
Should the Apple TV be disconnecting from your projector, try connecting to another device to test if the issue continues, or use a different cable.
Feel free to post an update for continued support.
All the best.