Hello tedpenner,
Here is my opinion, I have this crazy guess that Teatimer is actually running on your machine (you should check the Windows Task Manager) but [I think] there is some weird glitch (it does occur, but rarely on my machine) that Windows knocks the TeaTimer icon off the taskbar...
But I have this crazy idea (not certain if this resolves your problem, but you can try) to reinstall Spybot-Search&Destroy, reboot, and then uninstall again.
You did not have to uninstall Spybot for the TeaTimer :sad:, I feel you could have disabled it in the Advanced Mode (Spybot) and then re-enable it.