I can't hammer down exactly when this bug started in my project, but it looking back through different versions, it looks like some time after I deleted the initial room the editor starts you with, I no longer am able to add exits properly.
I can add one more exit, but any further exits I try to add the editor instead acts as if I have selected my most recent exit, regardless of what tile/room I clicked.
Also the 'place new exit' / 'click space in room to add exit' seems to stop toggling properly.
There was an exit in that initial room at one point. Is data from that exit not being cleanly deleted?