I get this problem too - but have noticed it seems to be worse in the few weeks after a major update (e.g. from Windows 10 version 1803 to 1809 or 1903).
After that the issue seems to settle down.
I did try the registry setting a few people have mentioned:
Computer\HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Control\Power
Change CsEnabled to 0
This made no difference so I changed CsEnabled back to default 1 setting.
*The problem has not occurred once since then.*
I have also looked in vain for the setting on the bluetooth radio and wireless keyboard in device manager.
e.g. In Properties, in the Power Management tab, uncheck "Allow the computer to turn off this device to save power".
However, on my Win 10 Pro 1903 there is NO power management tab on that properties panel.
I've navigated to the correct place, there just is no tab for that.
I've navigated to the same tab through the bluetooth settings applet too - and hit the "change settings" button.
No power management option there.
I even installed the specific driver for my bluetooth USB dongle from ASUS - expecting that the full driver would provide the power management tab - but it didn't.
Gave up on that idea.
So - from my experience, try changing the registry setting, reboot, change it back to default, reboot again.
Then make a wish, cross your fingers, promise to go to church (no need to actually go) and then hope.
Worked for me ;)