The malwarebytes tray icon appears only with the paid version with real time protection. It does not appear if you are running the free version. So if you have a paid version and the system icon is misbehaving, do the following.
1. Uninstall Malwarebytes Anti-Malware using Add/Remove programs in the control panel.
2. Restart your computer.
3. Download and run this utility as admin. http://www.malwarebytes.org/mbam-clean.exe
4. It will ask to restart your computer (let it).
5. After the computer restarts, install malwarebytes again. You'll have to reactivate the program using the license you were sent when you purchased it.