Same problem...all of a sudden this past weekend. Both the BT keyboard and mouse have worked flawlessly for 15 months. They get a LOT of use (5 in the family) and a lot of power on/power off cycles trying to extend battery life.
What I've noticed???
Flashing light is actually the "discoverable" piece of the keyboard when powering on. I think there is a timeout on it. I'm typing on it now, and the green light is NOT on.
I can pair after several attempts and toggles of the power switch (maybe 10 or so attempts). I also noticed that my BT wireless mouse becomes strangely
slow in response while the wireless keyboard is trying to complete the pairing. This would leave me to believe that it IS a software issue related to BT or OSX.
Also, once I get it paired, so far, as long as I don't turn the keyboard off, the pairing remains and the keyboard works. But when I turn the keyboard off, or if/when I restart the Mini (like after an update), then this process starts all over.
It's not the end of the world, but I am now looking at a new "wired" keyboard (I think) soon.