Bluetooth Keyboard Disconnects

On a recent 27 in 5K iMac, I suddenly started getting Keyboard disconnects, after I re-charged the Magic Mouse 2 & Keyboard. I'd had no problems prior to that. Following a period of Sleep, the only way I could Login back in was to connect the Keyboard with its cable, & use a separate USB wired Mouse. As soon as I was logged in, I could disconnect the Keyboard Cable, and both Keyboard and Magic Mouse continued to work, until the next sleep.

I then upgraded to 10.13.3 Supplemental Update, and followed advice to untick System Preferences/General/iCloud Handoff, which gave me 18 hours of zero problems. When actually working, the Signal strength for the Keyboard and Mouse is usually better than -50 dBm. -46 or -47 being typical. Since I have the Energy Saver to activate after 10 minutes, and put the screen to sleep, I discovered the Screen Saver was set to activate after 20 minutes, so I stopped the latter. I've also turned off my 2.4 GHz WiFi, & have experimented with aluminium sheets to screen external hypothetical interference, as well as using a WiFi Signal Analyser.

Now I have a situation, where Bluetooth works following a sleep, most of the time, so I can log back in, but as soon as I've done a little typing, I lose the Keyboard connection, and with the Mac busy trying to find it, it appears to completely ignore the Mouse, and often lose it too. I have to connect the Keyboard via USB, get the Mouse working, then unplug the USB connection to the Keyboard and hope it continues to work via Bluetooth.

Today the Bluetooth Icon on the menubar even stated: "Bluetooth Not Available" after a Keyboard loss. Opening System Preferences/Bluetooth fixed that issue.

How do I or Apple fix this problem?