Update: Haven't used my lemmy.world account in a while, so thought I'd test this out over there. Same thing happened after several minutes. Then I tried on Mastodon.world for a while and it seems to work fine. I'll try giving the alternate front end another round of testing later today.
Addendum: Can't reproduce the problem on t.programming.dev today, and couldn't seem to on a.programming.dev yesterday, so it seems to be specific to the default Lemmy front end.
I think I figured out how to reproduce it really quick.
Log in to Lemmy on Firefox
Switch to a different app
Switch back to Firefox
Reload the page.
Poof! I'm out. I repeated the test multiple times to confirm it's consistent. Probably actually getting kicked out on step 2. It's like FF decides to expire the Lemmy cookies when the app loses focus.
Armed with that info, I retested two alternate front ends on programming.dev (a. & t.) and default front end on lemmy.world and default front end on programming.drv with Brave. I was previously getting logged out on lemmy.world, but not now (maybe they updated something? Or my test is still flawed.). So, with these steps I can only reproduce it on programming.dev with the default front end on Firefox.
I seem to have isolated the problem to using a link to the website on the phone's home screen (created from FF using the "Add to Home screen" option in the three dots menu next to the address bar.
Starting that way seems to give any session cookies a very short life and they disappear quickly (logging me out). I created a bookmark within FF and have been using that and haven't been logged out since.
In fact, if I use the home screen link to programming.dev, FF doesn't think I'm logged in, but then if I use the bookmark from within that same instance of FF, it instantly sees me as already logged in.