CSS getting messed up

We’ve been having an issue where when Comet Cache is turned on, it’s intermittently messing up the CSS on the front-end. It’s been pretty hard to trouble-shoot because half the time things look fine, but sometimes it’s like a bunch of CSS is missing. The one thing we’ve been able to narrow down is that it only has the issue while caching is turned on. Any ideas what might be causing this?