I have just spend close to a month trying to track down unrepeatable behaviour in an application I am writing. The application is pretty hairy, and contains lots of matrices that are nearly singular, and I was imagining all sorts of weird numeric problems. But no. The problem was with the software that I installed for my Logitech video/web camera.
Essentially Logitech, in their wisdom, decided it would be a good idea to inject their lvprcinj.dll into everything possible, my program included. Something in that dll was causing unrepeatable behaviour in my program. Thank you Logitech for your malware. Problem solved. I for one will never buy a Logitech product again.