Know what? I think that might be a Safari/Apple problem. I am fighting that very same issue right now with one of the members on my website. She is the only one using Safari on an apple mobile device... ipad. And this is happening to her a lot.
I have done everything I can with the site yet it is still happening. And only to her with the Safari and the apple device. The “remember me” will not work for her at all, and even page changes kick her out. So I am now leaning heavily towards the problem being on her end and browser.
Thank you for a great response!