How do you get to the site on your phone? Are you using a shortcut or a bookmark or typing it in?
I have two thoughts, no idea if they're what's causing your problems, but maybe somewhere to look.
1) If you're logged in under https, then you use a link that starts with http, the cookies won't be shared and the 2nd link will ask you to log in again. When you do, you'll be logged out of the first session - the software apparently won't let someone be logged in on two separate sessions and/or devices (not the same as having several tabs open). Suppose you logged in via your shortcut under https and someone posted a link in the forum to another post using http. When you go there, you'll have to log in again (under http) and that will invisibly log you out of the first session. You can continue your session, and all will be fine. The next time you use your bookmark, though, it will have been logged out and you'll have to log in again.
2) Do you ever use another device - a PC or a tablet, maybe someone else's phone - to access the forum? Possibly there's something corrupted on the other device that is interfering with clearing the login cookies there when you log in on your phone and that's causing a problem when the other device says hello to the internet. If so, then perhaps clearing cookies and cache on THE OTHER device might help.