If you're still having trouble try this Phil, its worked for me.
1 - Carry out the advice regarding going to Device Manager - Human Interface Devices - Bluetooth Low Energy GATT... - Power Management - and uncheck Allow the computer to turn off this device to save power...
2 - Then also go back to Device Manager - Bluetooth - Power Management - Qualcomm Atheros QCA61x4 Bluetooth - click that and uncheck the Allow the computer to turn off this device to save poweroption.
Hope it works for you. Regards.
Mike.
Thank you MIKE! This was driving me nuts. So sad that Microsoft couldn't help or solve the problem. Mike's solution works! And I decided to try it *without* rebooting my Surface 3 laptop and I have not seen my bluetooth mouse (Logitech MX Master 3), keyboard (Logitech MX Key ), or headset (Aftershokz Aeropex) disconnect since I toggled that setting off... and it's been over an hour... it was connecting/disconnecting about every 5-10 minutes before it seemed like, maybe it was a tad longer. But definitely not happening now.