I've been having this issue for over a month and it's driving me insane. I have to waste so much time trying to get it to work. Mainly it starts after I start a new project and try to preview to see where I need to cut the video and it just sits there and does nothing when I press to preview. I've randomly got it to work by closing AE repeatedly until it finally works. It's a major waste of my time. I've tried messing with how much ram AE uses, I've purged memory and disk cache repeatedly. I don't know what else to do.
Nobody can tell you anything without some actual useful info. Sorry, but you have not told us anything that would allow someoen to help you such as system info, exact version of AE, preview settings, what your comps involve and so on.
And What my comp involves is just 1080p recorded gameplay that I use to make YouTube video's.