On the last day of a journey on the Alps, my NEX-6 started showing "Reinsert the memory card" and refused to work. The memory card, of course, is the same I've been using with that camera for a few years. I suspected it was a problem of dirt on the contacts, or in the camera: I blew some air inside, and inspected the contacts. The problem was still there. Fortunately, working with three camera bodies the impact was minimised. When I arrived at home, I tried the memory card with my laptop, and it was ok. The day after, even the camera accepted the memory card with no problems.
So, what would you do now? It might have been just a transitory issue (I hate transitory issues with no explanations, but technology forces us to accept them every in a while), or a worrying signal that something is going to fail, with possible loss of photos. The point is: is the problem with the camera or the card? In the latter case, it would be just a matter of a few euros, I'd prudentially just replace the card. In the former case, I should send the camera to the technical assistance. How to run a test and understand which kind of problem is? Honestly I don't have experience: I've never seen a partial failure such as this. In the past I saw a camera and a lens that just stopped working from one hour to the other, and they were completely dead; I never seen a failing memory card (with the exception of one I prudentially got rid of when I saw some cracks in the plastic near the contacts).