Apparently High Sierra has well complained issues with bluetooth. My Logitech MX Master mouse also suffers from random disconnection. Today when I tried to disable bluetooth and reconnect, the mouse just won’t connect.
So I deleted it from MBP’s bluetooth devices, and found out that MX Master cannot pair any more again. Just like some other guys’ video shows, it keeps connecting and disconnecting when pairing.
My old tricks in Yosemite did not work again, resetting the bluetooth module and remove all devices got no help after restarting the machine. Finally a glimpse of some words in some forum threads googled just saved my morning: complete shutdown, not restart.
Oddly enough, after a shutdown and fresh booting, my 10.13.6 High Sierra successfully pairs with MX Master!