Q: AirPort Utility and AirPlay no longer works after 10.9.2 upgrade.

Try running the combo updater.

10.9.2

I've lost Airplay in the past, I ended up having to reboot my wireless router, problem solved.

This worked for me.

Joseph Rose's solution (in another discussion) finally fixed Airplay for me.  I now have mirroring and extended Airplay functions again.  It was a long road, but in the end, removing Air Parrot and Air Display was the solution for me.

Solution:

Ran the Air Display uninstaller that I found by searching in spotlight.

Ran the Air Parrot removal tool & confirmed that the files were deleted based on instructions from their website.

Thanks to all that participated and spent their valuable time offering assistance!

Did you get it to work?  I'm having the identical issue - my iOS devices "see" the Airport and can connect to it via the Airport Utility app for iOS, but neither my MacBook nor my iMac running 10.9.2 can even see the Airport device, even though they are connected to the network that it's broadcasting.

I applied the OS X Security Update 2014-002 on April 23, and Airport Utility now "sees" my Time Capsule and Airport Express.