Thanks for your initial suggestions. I'll look into those settings and see if I can find anything.
In answer to your question, let's say you draw a 1 mm line, and then at the end of that line you try to draw a connected line at 90 degrees that is under 3 microns, when doing this the line will vanish the instant you complete the line. Anything over 3 microns, like 0.030001 mm will work, but 0.03 mm and less will not work.
Interestingly, if you do not draw a line that is connected to anything you can draw it as small as you'd like. It's just when you try to draw a line that is under 3 microns and is connected to another line that it will disappear.
I said submicron in error. I didn't do any tests before I made my initial post and just assumed submicron lines were vanishing. Now that I've done some experiments, the correct length is any line connecting to another line that is under 3 microns.
Lines will vanish as well when scaling them down using the scale tool. I don't know the details of this as I haven't done any tests, I just know that they do.