I cannot reach my ATV3 anymore after update MBA (late 2010) to 10.9
Have you made sure that your Apple TV (ATV) has the latest firmware?

Do you have another Mac you can try to connect to the ATV?

If you have another Mac then you could also try running AirServer (they offer a 7 day free trial) on it and see if the Air can AirPlay to it.

You need a little more information about exactly what is going on before you can really find a solution.