Chances are you've paired your Apple IR Receiver with a single remote control (in which case only that one will be able to wake it up) or turned the receiver off (in which case no Apple Remote will be able to wake the mini). Solution there would be to "Unpair" and enable the IR receiver respectively. You can find these options either directly in Remote Buddy > Hardware > Built-in Receiver - or - in System Preferences > Security > Advanced… (or "More…").

If that's not it or you want me to have a look, please run Remote Control Diagnostics (free download from the Labs section of this website) and copy and paste the full report it generates.