You can rest assured that Windows 8 and AOEO are compatible, as I use this combination daily to play. As for the issue you are experiencing, next time this happens, could you possibly open up Task Manager, and under the Processes tab see if the following exist:
Age of Empires Online Launcher
Age of Empires Online
If you're running Windows 8 64-bit, each will be followed by (32 bit). Also, is this install fresh from the manufacturer, or is this an install that you performed?