Won't detect Logitech Bluetooth mX900 mouse unless moving it at startup

When I start up my iMac, it does not automatically detect my Logitech MX 900 bluetooth mouse unless I am moving the mouse around at the right moment. If I am not moving the mouse, a screen pops up saying the computer has been unable to detect the mouse, and doesn't detect it until I move the mouse around (sometimes it takes 3-4 tries before it detects the mouse). Moving the mouse before start up (ostensbly to wake up the mouse first) does not help. This doesn't happen with the mouse that came with my iMac, but I prefer having the buttons.

I have gone through the bluetooth set up several times and have set the preferences to automatically detect bluetooth devices, but still my mouse hides from iMac! Has anyone else come across this and figured out how to make iMac automatically detect the mouse? I like to be able to push the on/off switch and walk away while the iMac does its start up, but I feel like my cordless mouse has become an electronic leash from me to my iMac!

Logitech doesn't offer drivers for iMac for this particular mouse.

Can anyone recommend a better optical cordless mouse for iMac that doesn't have the same issues?