Ok, so I just tried it on my iPad, which is running iOS 8.0.2 (haven't applied the latest update yet), and I don't have the issue that you're describing. I accessed Finescale.com on Safari, entered my username and password, got logged in, then I exited out of Safari, went back in to Safari, went to the Finescale.com page, and I was still logged in. Is that what you're having an issue with?
Devil Dawg
On The Bench: Tamiya 1/32nd Mitsubishi A6M5 Model 52 Zeke For Japanese Group Build
Build one at a time? Hah! That'll be the day!!