Boffin1:
I had a similar problem with cascaded LED drivers ( mine were latched shift registers but it might apply ? )The current for the LEDs was returning through a small connector and wires to the power supply, and the slight voltage drop was corrupting the data, by hooking all the grounds and supplies with a separate pair of wires to each panel cured it in my case.
That would do it...
A voltage drop along a ground wire would mean Arduino ground wasn't the same as one of the panel grounds. Good grounding is essential, this is the sort of thing that electronics engineers from mere mortals.