MacOS Monterey + A1016 keyboard short battery life?

I upgraded to an M1 Mac Mini earlier this year and sadly I discovered that my trusty Apple Keyboard (A1016) would not pair! After researching the issue I found some information that involved using "blueutil" to complete the pairing process... it worked! The keyboard works great, with one exception, it now drains batteries... I've used 4 rechargeable eneloop AA batteries for years and they use to last 1-2 months or more, now I am changing them every 3-4 weeks. I suspect that something is preventing the keyboard from entering a low power / sleep state.

I am thankful that the keyboard is at least still working, and I can deal with changing the batteries often but it would be amazing if someone at Apple would look into fixing the compatibility issue with their own keyboard!

PS. I will buy a new keyboard when you make one that beats this old A1016!!!