Fair questions 
The code: https://github.com/ReallySmall/Stackduino-2/blob/master/Stackduino_2/Stackduino_2.ino
The oled is this one: Mono OLED--0.96" Serial: UART/I2C/SPI 128x64 OLED Display Blue DS12864OLED-2B...
It uses a PIC18F26K20-I/SS to control the screen: http://ww1.microchip.com/downloads/en/DeviceDoc/41303G.pdf
I'm using the screen in SPI mode and calling high level functions (https://www.digole.com/images/file/Tech_Data/Digole_Serial_Display_Adapter-Manual.pdf) rather than talking to the screen directly. It's all quite abstracted, which is great when it works, but seems hard to debug when it doesn't....I don't really know what's running on that chip or how to find out if there's anything wrong.
I've tried the sketch with multiple boards and several other sketches, short and long, including the examples from Digole. So unless I'm wrong, I think I've ruled out my hardware and my code. I don't think it's an out of memory problem as even very short sketches exhibit the same problem.
I've been talking a bit more with Digiole about it today and there's one suggestion that it might be down to the default font being corrupted. I've tried switching to one of the other preloaded fonts in my sketch but that doesn't appear to work.
Puzzling.