I don't often use continuous AF, but needed it at the weekend chasing a 9 year old on a swing. I switched to continuous and then nothing happened. It locks, confirms focus and stops exactly as in single shot. As an old CF4 Canon user, I have AF disabled on the shutter button (beats me how you can work with it enabled), so I activated shutter button AF and continuous now works.
To my simple mind, that is a bug. If I can disable shutter button AF for single shot, why not for continuous? If I am missing something, I would dearly love to be shown how to get it going.
I have also had a very rude awakening with Sony. With Canon, I had CPS that I could go to. I'm not aware of a Sony equivalent. I rang a number that I was given of a tech guy in Sony, but he hasn't bothered to return my call after 2 days. I hope that this experience is not typical of Sony generally. It make me appreciate how great Hasselblad is in their customer dealings.