Q: Every time I turn on my Mac Mini my keyboard needs to be reconnected.

Is it an Apple BT KB?

Try:

Troubleshooting wireless mouse and keyboard issues

  OS X: Bluetooth devices become unresponsive

Could be. What do you do to reconnect it?

Do you have another computer or KB to try?

Try disconnecting all peripheries.

You could try deleting the bluetooth plist file. That might work.

With Finder active, hold the Option key down and click Go in the menu bar. Select Library.

In Library scroll through to Preferences and look for the file called: apple.BluetoothFileExchange.plist

Move this file to the desktop, and restart the computer.

You will have to "pair" the mouse once again.