And what version of AE are you using?
And what are the rest of your system specs?
I’m using version 22.214.171.124
iMac Mid 2011
AMD Radeon 6970M 1024MB
This thread seemed to find a solution, but you're not going to like it...
I'd recommend being as aggressive as you can with other solutions first, such as fixing permissions problem that impedes start of Adobe applications on the off chance that they help.
This thread on App Nap causing issues would also be worth a look.