I have also been fighting with this issue of the admin bar login plugin not working with current the wordpress dynamic admin bar. Any time the display size shrinks all content disappears, mobile or not.
After taking 2 days to look over the back end of things, I can honestly say that it's going to take more than a simple CSS call to get this working while *not* breaking the minimization that WordPress has implemented.
I'd like to put a vote in to have this plugin updated to take advantage of/use the minimization as it affects 1/2 screen desktop browsers as well as mobiles.
Unfortunately, as it stands, I'm going to have to turn this off and use a different, widget based login system until it can be updated. Annoying since I really like this plugin, but that's the way it bounces.