Bad Gmail, bad!
I had this same exact problem; after rooting and installing Google apps (Play Store, Gmail, Maps, etc.) my notification and soft bar menu hadn't completely disappeared, but it would pop up occasionally (and randomly), but of course never when I needed it. After some searching on the web, and a lot of digging in this forum, I also found and confirmed that it was Gmail of all things causing my problem.
I uninstalled Gmail(Kindle has an all-in-one e-mail app of its own, so I don't really need/care that Gmail is gone) and rebooted, and my soft bar menu and notification area are both back, without any problems that I can see (so far, anyways). So anyways, try it! Looks like uninstalling Gmail worked for a few of us here~