I use Airfoil to make it easier to sound from any audio source on my Mac to as many speakers as I want (something you can only do normally in iTunes), but I’ve noticed the sound dropping out frequently since updating to OS X 10.9.
Rogue Amoeba’s release notes don’t hold any clues besides the fact that Airfoil is not yet Mavericks-compatible, but I realized that the sound seemed to resume whenever I would switch back to Airfoil to see what the problem was.
Enter App Nap. Of course Mavericks has a marquee feature that explains just this behavior. App Nap “pauses” apps that it thinks are running in the background and needlessly taking up resources. A quick search lead me to an easy way to prevent OS X from putting a specific app to sleep.
Open /Applications in the Finder, select Airfoil, and hit ⌘-i (or Get Info in the File menu), then check the “Prevent App Nap”box under “General.”
That seems to have prevented the sound from cutting out for me.