No set the exe properties to run admin under compatibility. Then the launcher will launch it admin as it starts. Ensure you do that to the x64 exe if you're using 64 bit arma.
Sounds more like a write/permission problem with where ever your Arma 3 profile is located. Arma 3 normally writes those presets into a file to do with your profile to save it. If this is in an area Arma 3 has no permissions to write to then it wont work - try running Arma 3 or even Steam as admin before launching the game, set the controls then it should save them?