What do you mean when you say your audio "cuts off"? Are you playing music through a program and it stops playing? Does it play again when you switch back? Are you previewing audio and it stops playing? Are you saying it just makes your audio stop working on the whole computer until you reboot? Are you saying AE won't play audio after you switch to another program?
Also, what exact version of AE (down to the last decimal point)?
What are your system specs?
I'm using AE CC. Everything works fine in AE until I import audio. Once I ram preview everything works fine. Audio works fine. When I click out of AE into another program my computer mutes. (Sometimes I have youtube or iTunes playing in the background.) I then have into System Preferences and with the Output back to headphones. Oh, I'm using headphones.
What exact version (down to the last decimal point, please)? For example, at home I'm using 126.96.36.199 and at work I'm using 11.0.4.
What happens if you just use your computer's speakers?
How many audio output jacks does your computer have?
What are your computer's specs? Heck, we don't even know what OS you're using!
It helps a lot.
Note: you are not using the latest version of After Effects. The whole Adobe suite released new versions that you can download which will install alongside your current versions. After Effects, Premiere, Photoshop, and all the rest now have a CC 2014 version. It won't show up as an update because it's a whole different version number and not an update. It may fix your issue, it may not.
Screenshots of your audio hardware preferences in AE probably wouldn't hurt if the problem continues in the new version.
By the way, did this issue occur before you updated to Yosemite?
If not, it wouldn't hurt to check this issue out: fixing permissions problem that impedes start of Adobe applications All kinds of weird stuff happens when you update Mac OSX and the permissions get screwy.