I've just upgraded W3 Total Cache from 0.8.5.2 to 0.9.1.1 on my site.
Since doing this I've observed some problems for people trying to leave comments. After they have logged in and navigate through the site they sometimes appear to have logged out again. Navigating to a new page or performing a refresh clears the problem and shows them as logged in again.
I've been able to replicate this problem and if I deactivate W3 Total Cache the problem goes away. When I reactivate it it returns. If I activate it and turn off caching in the options, the problem remains.
I've also tried selecting "Don't cache pages for logged in users" in "Page Cache Settings" but the problem remains then too.