We had the exact same problem during the January exam - 1 out of 8 students taking the exam had it crash when she went to print. In the end, I just had to take a screenshot of the state of the exam at the point it crashed and submit it along with an explanatory note.
I don't think it's an issue with the version of Flash Player installed on the computer (we always keep it up-to-date). Bear in mind that the Flash Player is a browser plugin, whereas the AQA exam runs from a Flash projector, i.e. the standalone player you can generate when a project is exported from Flash. The executable uses its own internal version of the Flash player dependent on what version of Flash the project was built in, so it works independent of whatever browser plugin you have installed (and even if you have no plugin installed at all). I quickly checked the executable for versions of the exam software going back to June last year, and they all use 10.1.52.14.
But yes, this is quite a serious issue if the exam software is unstable.