Unticking the "Remember Me" box when logging in "fixes" the problem - but now I get logged out after a short amount of time (even though I haven't closed the browser in the meantime, and even though I have the "store cooking for 1 year" option set).
So I guess that (a) for whatever reason I'm getting logged out after a very short amount of time, and (b) the "Remember Me" option causes a redirection to the Amiga.org front page, somehow wiping the history of whatever page I was looking at.
I don't know if it is a browser problem - I'm using Opera 7.50.