Don't know if this is an issue with AE in Mavericks, but it was posted as an issue over on the FCPX Debate board. It seems that when rendering, FCPX was stopped by Mavericks' new App Nap feature.
There is a fix: Just go into Applications, highlight the AE icon (or any app, actually) and hit CMND-I or right-click and select "Get Info." Check the box that says "Prevent App Nap" in the top "General" part of the info window.
I have read this a lot online, but, when I click on my AE application, I do not see the Prevent App Nap. I found it on my Premiere application, and the AE Render Engine, but not After Effects itself. Does anyone know what I may be doing wrong?