When I used an ethernet cable to set up the A1264 (because AirPort Untility did not "see" the Express on WiFi), it did join the extended network
If you connected the Ethernet cable from your AirPort Extreme to the Express, then AirPort Utility thought that this was the way that you wanted to set up the Express permanently, so it configured the Express accordingly....to connect using Ethernet.
As soon as you disconnect the Ethernet cable, things won't work.
The real issue here is that AirPort Utility did not see the A1264 Express wirelessly. If you want to configure the Express to connect to the network wirelessly, then that is the way that you must set it up using Airport Utility.....wirelessly.
Try a Factory Default Reset on the A1264 Express to see that will allow AirPort Utility to see the Express wirelessly, so you can set it up that way.
Power off the Express for a few minutes
Hold in the reset button first and keep holding it in for an additional 10 seconds while you simultaneously plug the Express back into power
Release the reset button after the hold period and allow a full minute for the Express to restart to a slow, blinking amber light.
Then try the setup again.....wirelessly. If AirPort Utility still cannot see the Express after a few reset tries, the Express is likely defective.
As a last resort, try connecting an Ethernet cable from your Mac to the Express and try to set it up that way. If AirPort Utility "sees" the Express this way, you might be able to set it up, but this also confirms that something is not right with the Expess. You should be able to "see" it wirelessly using AirPort Utility.