@Vlad I managed to record the issue. As you can see, search displays the login screen, and after login the initial query is lost.
From what I see, it seems to occur only when searching directly after firefox has been inactive.
But to add an info, while I was typing this message, I had left the phone, and during that time, the page with the results of my initial search had opened up. So the issue is not so much that the search is lost, but that it takes a long time (many seconds?) to be re-submitted after login.