Logitech MK850 and M720 BT disabled @ login upon restart/startup

I have a Logitech MK850 and M720 keyboard/mouse combo. I use it for combination windows laptop (via Unifying Receiver) and MacBook Air (via bluetooth). The issue is that on the MacBook Air, I am unable to use the keyboard/mouse at login after restarting the MBA or starting it up. I have to usually, use a the keyboard on the MBA itself to the login. I converted over to the MK850 from a Logitech K811 and a Ultrathin mouse. The K811 always worked at login after startup.

I tried bluetooth connecting on another Mac that I have. Every works as expected, including login after startup/restart. I can logout on the MBA and then log back in okay on the MK850, but just can't after startup/restart.

I have tried zapping the PRAM twice, deleting plist files to have the MBA re-create them. Also tried holding down the caps lock key. Nothing seems to help resolve the issue. But I just do not know what to do at this point.

I believe there is something going on with the MBA itself and can use any suggestions.