I am having a similar problem today, using an iPad Air with the Safari browser (all updates). I have stayed-away from this site for a while, due to the NUMEROUS log-in and performance issues with the site.
When I go to the home page and log-in, I get the welcome log-in message, then I am promptly logged-out.
I was able to select the forms, this forum, then log-in to post this message.
Why are these problems continuing? When will they be fixed? Thank you.
The only way I have found to remedy the problems is to make sure you check the :Remember Me: box before logging in.