That's nothing that has anything to do with GSX, of course. GSX menu is a STANDARD FSX Simconnect menu.
So, your question should be more like: why EZCA doesn't respond to key presses when another standard Simconnect menu is open ?
My *guess* is that this is caused by that program use of a non FSX-standard way of handling the keyboard, instead (like we do) to rely on the standard FSX event system ( we don't read or process the keyboard directly ), which would explain why some users of it reported about issues and solution.
Your best option would be reporting this EZCA developers, or ask to other users. The only thing sure, is (assuming if you are SURE you assigned GSX to keys NOT used by EZCA), it's nothing that has anything to do with GSX, which doesn't handle the keyboard directly, and it uses a 100% fully standard Simconnect menu, so it's very likely you'll have the same problem with any other FSX addon that creates a menu in the same way.