There were a few posts in the recent past about this. appletv2, can't start a movie and than back out of it and start another one "or the same one". you have to reset the box, or even in some cases wait 10/15 minutes. There were a few people claiming to have the same problem both on this site as well as in general google searches.
I fixed it on my side. I'm guessing there could be other reasons, but this is what happened to me.
Wireless Router had a 192.168.2.X subnet mask and the actual Verizon Modem has a 192.168.1.X subnet mask.
I forced the Wireless Router to be in the same subnet mask and it's fixed.