Re-install the A/V software
Try another USB cable and USB ports. DO NOT use USB hubs, powered or otherwise.
Make sure you're only using DMX cabling.
What is your pre-show preparation procedure?
Make it this:
Disconnect the MyDMX hardware from the computer prior to start-up.
Boot the computer.
The MyDMX hardware should be connected to a USB cable and to DMX.
Once logged into your computer, now you can connect the MyDMX hardware to a USB port.
Lastly, now you can connect launch MyDMX.
MyDMX seemed to support Win7 better since April 2010. The first round of 64-bit drivers were designed for Vista 64, but have been tested to work with Win7 64-bit. You may have to use a more recent version of MyDMX to ensure reliability with Windows 7.