I had similar issues ... intermittent periods where keyboard (a K750) just didn't respond.
I resolved the problem by updating the keyboard firmware through the Unifying Software utility. On my Win 10 box I did these steps:
- Right click on Logitech system tray icon and click "Keyboard and Mouse Settings" to bring up the Logitech settings panel.
- Click on the asterisk-looking icon in the nav bar on the left to get to "Unifying Settings"
- Click the "Open Unifying Software" button
- In the Unifying Software dialog, click "Advanced"
- Select the keyboard
- If the "Update Firmware" button is enabled, then an update is available; click the "Update Firmware" button and follow the instructions.
- Select the mouse (if any) and "update firmware" if necessary.
That's it. You problem might, may, will perhaps be solved. Or not.