Hello, I am writing from Argentina .
I commented that the problem is solved .
I tell them I have a pro Mb of this year , and an Apple TV3, my problem was that I stop airplay icon appear on the top bar , and only reproduced video from iTunes. .
Now the solution .
apple tv plug it into my computer , and I program in DFU mode or restoration ,
SITE IN ENGLISH
http://appletoolbox.com/2013/07/how-to-put-your-apple-tv-into-dfu-mode/
SITE EN ESPAÑOL
http://applediario.com/2010/10/21/como-poner-tu-apple-tv-2g-en-modo-de-recuperac ion-dfu/
start it in this way because in normal mode iTunes told me I was already updated to the latest version .
after downloading the new firmware ( 870 megabytes ), must be connected back to the TV, and configured with the installation wizard
that once completed , restart my macbook
macbook restart . and....
bingo!!
the mirror functions as before.
Apologize for my english , but as is evident I translated with google translate .
I hope this helps someone.
a greeting.-