[Comment removed by author]
I don’t know of any good quantitative research on that, but there’s some good qualitative stuff in writing from Jens Rasmussen and Richard I. Cook. I’d start with the classic “How Complex Systems Fail” (http://web.mit.edu/2.75/resources/random/How%20Complex%20Systems%20Fail.pdf), and follow on with some of Cook’s papers where he looks at some great examples of the problem.
Cook also talked about this at the Velocity 2013 conference: https://www.youtube.com/watch?v=PGLYEDpNu60
So when do simple systems become complex?
In my experience, whenever somebody has been told they’ll be maintaining them. :(