Okay, here's a new model. I was having issues with it yesterday that caused me to finally reach out and bother you. I spent the last couple of hours working with no issues, but finally ran into some. Like I said, this does not seem to be specific to any model, nor is is consistent within any model. I was finally able to replicate the issue and noticed that it does seem to happen when I am trying to move copy a single line from an edge within a face. I'm not sure now that you will be able to see anything as it took me a couple of hours to recreate, whitecoat syndrome I guess...
I use alt because it is the same as the option key on my computer.