My class still looses connection but I now think that the problem is between the classroom and the school web server. I think it's the school server that's not handling all the requests. If the Mysql database is failiing then it would take longer than a few minutes to restart itself. (I think) Also there are plenty of documented situations where Moodle is running in the midst of thousands of students and this problem is not occuring. Alternatively, perhaps there is an old switch still lurking somewhere in our system that needs updating.
Does this make sense?