I've discerned no changes in the sound signature of my Fidelio X1s after extended burn-in. Might update this with results from new JVC HA-S680s coming in a few weeks to see if any 'burn-in' is noticeable. I suspect advocates of burn-in are a lot like those who refrigerate their batteries. Human consciousness is not static. If you listen to some music today it may sound different the next day. Stress and various factors can affect our concentration. We can just as easily tune out certain aspects of music like we can tune out a lecture or the sound of a road nearby. It's easy to attribute attribute accommodation to the sound signature of a pair of headphones to the burn-in process, but the science is just not there. Until there is a section on Wikipedia dedicated to and explaining burn-in, I categorize it with magical thinking. Most times I see burn-in recommended no one actually mentions what improved, but choose to use ambiguous terms like 'improved clarity'.
Does the audio crowd (audiophile is kind of an annoying term at this point that carries certain implications) really need more people who advocate things they can't explain even in the simplest of scientific terms? Some have equated burn-in to combustible engines, but really most electronics do not burn in but instead suffer from wear and tear. Screens lose brightness as they age, computers do not get faster from 100 hours of use.
My Arx-A1b's sound better than they did a year ago, but that's because I replaced the lepai2020 with a Topping TP-21. For sound quality to improve, you have to make a change to the design, such as replacing the cushions or the drivers, or adding a port. Some things really just work right out of the box people.