Though I notice I'm having the same problem (latest Chrome on iPad 2), it seems to be when I follow a link from GMail.
Get email update on thread, click "read this reply"
Chrome opens new tab
E asks me to log in
I log in
I read post.
Time passes..
Get email update on another thread, "click read this reply"
Chrome opens new tab
E asks me to log in
I switch to previous tab, hit refresh, page reloads OK
Hit refresh on new tab, login page clears, new reply loads.
Suspect new tab isn't recognising old cookies but I'm rather a novice when it comes to cookie handling.