Next, I switched the drawing to the Model tab and set the drawing scale to 1" = 30' and drew my own line on the same layer - linetype looked great, her polyline looked continuous. Hmmmmm. Not sure what made me do it but I used the BREAK command to break her polyline and voila! the linetype appeared.
Now, the linetype in question was a custom one that uses a custom shape. I think maybe there is a limit to the number of times that a pattern can be repeated within a given object (or maybe a shape inserted) but when you took this massively long polyline (76 miles) and tried to show it at a smaller scale (more copies) it said "Uh-uh, not doing that." The solution was simply to turn the 76 mile polyine into as many shorter ones as needed by using the BREAK command or whatever other command you fancy.