I have the same issue, but I am connecting to my desktop computer/ PC via a bluetooth dongle. The Precision mouse does not lose connectivity, but the keyboard does, after a few minutes of inactivity. Then I have to go to settings, remove it and re-install it. It is very, very irritating and costs me a lot of time.
I tried both of the above, The former did not work because the Power Management tab did not show up. I tried the second approach, through Device Manager, did find the power management tab, made the changes, but to no effect.