Launchpad keeps rearrarining icons
I don't know what you've tried thus far but a solution I've found to work well in the past for Launchpad issues is just to force reset the Launchpad back to its default settings. Most people don't enjoy doing this because it requires you to then set everything back up the way you like it afterwards, but at this point that's what you're having to do after every restart anyways, so what have you got to lose?

To force reset Launchpad back to default settings:


Launch Terminal.app
Carefully type the following: defaults write com.apple.dock ResetLaunchPad -bool true; killall
Wait until you notice the Dock refresh; this means the process is
complete


I would then only move a couple things around in Launchpad for time's sake (in case this didn't work) and then restart your Mac to test!

If that did not work, simply force-resetting may have not be enough. Maybe it wasn't just the defined settings inside of the file that were corrupt, but the entire file itself. If this is the case, we need to delete/remove the file and trigger the OS to create a brand new one. You have two options for this!

Option A)


Navigate to ~/Library/Application Support/Dock (yes, Dock!) 
Move any files in this folder to your Desktop (except for the one called 'desktoppicture.db' if one is present)
Restart the Mac
Move a few app icons around in Launchpad to suit your liking
Restart the Mac again to test
If the issue is resolved and no new problems occur you can move
the files(s) we relocated to the Desktop to the Trash; if issue still occurs (and especially if any new issues are occurring), move the file(s) on your Desktop back into the ~/Library/Application Support/Dock folder and choose "Replace" if prompted, then restart your Mac.


Option B)


Navigate to ~/Library/Application Support/Dock
Move 'desktoppicture.db' to your Desktop (if the file exists)
Launch Terminal
Carefully type the following: rm ~/Library/Application\
Support/Dock/*.db ; killall Dock
Restart your Mac
Move 'desktoppicture.db' from your Desktop back to
~/Library/Application Support/Dock (if it was present in the first place)
Move a few app icons around in Launchpad to suit your liking
Restart the Mac again to test (your background should also be back to normal if it had been changed during this process)