iOS 8 for iPad 2: Closing a tab in private browsing causes me to log off from sites in other private tabs

I just upgraded my iPad 2 to iOS 8. I was previously using iOS 6, so bear with me, as I'm obviously way behind everyone else.

I find that when I'm using multiple tabs in private browsing while logged on to a social media site or a prescription newspaper site or whatever, if I close one of the tabs, I log out of the site. I used to be able to close individual tabs without logging off whatever sites I was on.

Is there any way around this?

Thanks!