Yeah, it is. It's had us scratching our heads, here, too.
The only other things I can suggest are that you adjust the cookie length setting, in Admin>Server settings>Cookies and Sessions.
In the same place, you'll see:
Enable local storage of cookies
(SSI won't work well with this on.)
Use subdomain independent cookies
(turn off local cookies first!)
One will be checked and the other won't be. You could try swapping those over.
Also, there's "Use database driven sessions", which you could, again, switch over, and "Seconds before an unused session timeout". You could always try increasing that.
Bit of a minefield, I'm afraid.
By the way, if the Chrome user wants a version that doesn't spread their private details all over the net, let them see this:http://www.srware.net/en/software_srware_iron.php