I'm currently experiencing an issue on SP 2010 and anonymous sites. Sometimes I am unable to stay logged in.
On an anonymously accessible site, when trying to log into the site, the page seems to only refresh. Continuing to click sign-in will eventually get the user signed in. But after navigating around on the site or hitting refresh the user will go between being signed in and signed out. Visiting a different site within the same farm and from the same server results in the correct behavior and the user will stay signed in. Most of the time closing all IE windows and reopening the site will fix the issue. I have seen this issue happen on IE9 and IE8. Others have reported to me that the issue happens for them on Firefox and Chrome as well.
Here is a screen capture video I took of what happening: https://partners.myskanska.com/Shared%20Documents/ScreenCapture_11-30-2011%2010.28.13%20AM.wmv
Any thoughts on what could be happening here? I'm on SP 2010 Enterprise SP1 and using Windows Server Network Load Balancing with single client affinity.