I've been having this problem with AE 13.5 & AE 13.6 (2015 versions). 13.2 does not do this...
When I start a new project, I can do everything normally including rendering a file once. When I make changes and attempt a 2nd render of the same project, After Effects freezes. If I close the project then re-open it and try to render it freezes.
Here's where it gets interesting...
I can open the same project in AE 13.2 (2014) all day long and make adjustments and render just fine.
There is a new setting or something introduced in 2015 that is causing me issues. Or more likely, user error.
Intel(r) Core i7 950 @ 3.07 GHz
48 GB RAM
Windows 7 Pro
Nvidia GeForce GTX 980 Ti