I have the same problem with my Magic Mouse, and the suggested solutions in this thread have not solved the issue.
If I turn on my Magic Mouse, the only way to get it to reconnect is manually either via the Bluetooth System Pref panel, or using the Bluetooth menubar item, both of which require a wired mouse to do so.
I have my Magic Mouse set as a Favourite, and I have tried switching it on and then clicking it, to no avail. It's the only Bluetooth device I have.
For the moment, my workaround involves a key sequence in iKey that does the mouse-clicking for me, but there must be some reliable way to get the mouse to reconnect automatically with the iMac? I'll try deleting the mouse from the list and recreating the pairing, see if that helps.