Chasing a 'Bot Instability

My 'Bot has developed a bit of emotional instability.   Or instability anyway.   It runs for a while and then without fail loses it's network connection.   It seems to have started with the introduction of the LCD...but...the LCD is connected to the Arduino not the RPi!   I have also added another GPIO function but the network crash seems to happen with or without the GPIO functioning.

I have started a series of tests to try to narrow down the source of the problem.  So far I have tried running with and without the GPIO functionality and with and without the LCD functionality.   I have also let the RPi run without my Python code but with the camera and some other processes running.   In the former two cases we had a failure in the latter we were stable.