It does seem to be pretty random (or at least hard to say what causes the issue to manifest itself.) From reading through the threads, some people plug in and have issues immediately, others seem to get them later on and others don't seem to have them at all.
For me, once they started they became much more frequent and began to get worse. Black screens would usually clear themselves after a few seconds but then they became the snowy/static screens and cycling inputs/powering off the HDTV didn't clear them and I had to reboot. I returned my Mini (albeit with a heavy heart) on day thirteen and got a refund. My first couple of days were via DP to DVI and I didn't have any issues at all, then I ran the Mini on a Samsung HDTV for just over a week on HDMI and on day eleven, right out of the blue, the problem started.
I hope your Mini remains problem-free, anyway. 🙂