WooZie, it happened to me, too. Then if I turned off the Mini and waited a few minutes before try again, the MM started up normally. I am quite sure the reason for the intermittent no response problem is that when you turn on the Mini and let it sit around for a while, its processor gets overheated (as it does not have a cooling fan inside), and it does not let it start up. (If it was connected to a phone and the Fly app, you would get an overheating message as well).
So try to turn it off and wait about ten minutes, then turn it on again and try to start up with the remote as soon as youpaired the two.
Just my two cents...