I recommend leaving the brake on for normal cleaning with the muzzle down. after cleaning I spray it with WD40 to remove any remaining solvent. Then I use compressed air to blow out any WD40 and finish up with Q Tips on the brake and dry patch the bore and brake. wipe the barrel and brake down with an oily rage for storage. After a few shooting sessions, if the brake looks like it is not clean, it can be removed and cleaned using solvent that removes carbon and/or an ultra sonic cleaner.
NOTE: I don't recommend brake cleaners or carb cleaners because some can be harmful to certain grades of steel.
If you remove the brake, clean the threads on both the barrel and the brake and apply a good Anti-Seize before re installing. if you don't have a torque wrench or don't know what the torque was when installed make a small mark/scratch on the bottom of the brake and barrel and then just align them when you go back with the brake.
If the brake is installed correctly it will make up fast and wont loosen with use.
J E CUSTOM