Hmm, that sounds like one of three things, either the supply voltage is too low on the second module (possibly related to my comments in the previous post), a noisy power supply or data line causing data corruption, or a bad cable or connection somewhere.I note that once loaded, if I press the boards reset button, the second display flashes all segments momentarily, but blanks and leaves nothing on the display.
When you swapped the modules around did you keep the cables in the same order? If so, are you able to try a different cable between the first and second modules just in case is a bad cable between the two?
Also, do you have a volt meter that you could check the VCC output pin on the second module with? Failing that here's a couple of things you can try to see if it's the supply voltage being too low to the second module:
Connect a separate 5V supply from your Arduino to the VCC pin on the second module rather than linking it through the first module. You can keep the GND connection daisy-chained through the first module if that's more convenient. If you’re using an Uno you can get a separate 5V from the IOREF header (edit: 5V Arduino only) or from the ICSP header.
The other thing you may be able to try is to short the diode on the back of the first module (should be marked D1) with a wire, paper clip, or tweezers then write to the modules again.