Here are a couple of suggestions:
First, find out where the power loss (i.e. voltage drop) is occurring. Start at the back of the radio (I believe it's a yellow wire) and verify that you have 12V (~14 with the engine running) and that it is in fact dropping significantly when you roll the window down. That being the case, start working back through the wiring harness until you find a solid 12V signal.
While it is possible that there may be a problem with the express down module, any significant overload on that circuit should blow a fuse. What is more likely is that a connection (be it a harness contact or in the ignition switch) is failing, creating a resistance as the current through it increases.
Alternatively, try holding several of the other window switches down to see if that creates a large enough load for the radio to shut off. In the case of the accessory circuit, there is not really any other high current component to use as a check for a harness/ignition switch problem.
Let me know what you find out, or if I've said anything that is unclear.
Dave