I access the full site on my iPad, and make sure to always check the "Remember Me" box when I log in. And I have cookies enabled in iOS (and do not have problems with any other sites). But with FlyerTalk, after about half an hour, I have to log in again. It is very annoying.
My iPad used to remember my Flyertalk login. But then one day I told iOS settings to not store cookies. The next day, I switched iOS back to storing cookies, but since then, Flyertalk has not stored a login cookie for me.