@ billt - I used to have the same problems as soon as I started accessing the site through a mobile device. For me, I have to go to the amiga.org home page and sign in on there in the top right corner and tick the retention box. It then keeps me logged in forever, or until I sign out. It even lets me take ages and ages writing posts and it NEVER logs you out or times out when doing so.
However, if I am currently signed out and I try and reply to a post or view an attachment and it asks me for login, it's this instance where it doesn't work correctly. I think it works until you leave the thread, then it seemingly signs you out and your post disappeared...but your post is actually there (confirmed I think by the 'view 50 recent posts' link. This behaviour was on my Windows phone and Android.
So if you clear your phone cache/history and sign in on the home page with the tick box ticked, all your problems should disappear.