As @interolivary said, it’s not a you problem. It sounds like you’re using the PWA for Beehaw since you click an icon to open it. I’ve had this same problem on mobile using PWA (Chrome and Firefox) but not with desktop browser. I’ve also not seen this on the mobile apps I’m trying out (Voyager and Jerboa). From the symptoms it seems like closing a PWA session clears the browser cookie that’s being used for session persistence.
Try just using it from the mobile browser; I have not seen this issue it on Chrome or Firefox on Android and I expect that Safari on iOS won’t have the problem either.