Finally found the solution:
1. Reset the Launchpad in the terminal:
defaults write com.apple.dock ResetLaunchPad -bool true
killall Dock
2. Take print screens of the launchpad and the folder <Others>)
3. Reboot
4. Let the Launchpad to rearrange as it is. Don't do any arrangement
5. Wait for couple of days.
6. Reboot twice
7. If you see some apps are missing in Launchpad, drag them to Launchpad from Apps (in the Finder call the list of app: shift+command+A)
8. Reboot once
7. Check whether missing apps appeared in the Launchpad
8. Reboot once more time
9. Check whether the Launchpad stays as it was before.
8. Now rearrange Launchpad as you wish and you save to reboot as much as you needed.
This worked for me and now stays solid. I have to reboot on daily basis due to Bloomberg terminal under bootcamp partition, so no issues at all.