When you create a new question, related questions takes up space and this pushes the content of the page downward. For keyboard only users like myself, and for my screen size ... this causes the Tags area to move downward as well. This is not a problem in itself, except that when I get into the Tags field, the "dropdown" assumes always that it should dropdown and the contents appear offscreen.
Another potential resolution would be to scroll the page on entry into the Tags field to ensure that some of the dropdown contents appear.
Another solution would be to give the Tags presence higher up on the page.
UPDATE: You could simply reproduce this by resizing the window so that Tags field is visible but nothing below it. Then start typing a tag in the field itself. Since it drops down, it is invivisible. On the surface this would seem expected, except that the page itself is chewing up real estate for related questions causing everything to be pushed downard.