Problem is resolved!
Yes, the item "Show SUPERAntiSpyware icon in system tray" was already checked. I started to uninstall, then re-install, but when I went to add/remove programs, SAS was not even listed. Something must have gotten corrupted somewhere.
I resolved the issue by downloading the most recent version (which was the same as what I had been using) direct from SuperAntiSpyware.com. Next I installed the program, entered my serial number, downloaded the latest definitions, then all worked normal again after that.
Thanks to all who replied. I hope this helps someone in the future.