If the barrel is a stainless alloy and the brake is a carbon steel alloy, there is the possibility that either thermal cycling or galvanic corrosion have caused the threads to become fixed.
My suggestion would be to use a propane hand torch to heat the brake in a line on one side only (to get it to expand and open "like a door"), not the entire mass, in order to minimize concurent heating of the barrel. Proper fixing of the barrel in a vise makes handling easier. If/when it breaks free, if there is any continued binding resistance, resist the tempation to screw it completely off in one go, rather, twist back and forth with progressive removal, like tapping threads in a hole. This is to avoid galling the softer stainless thread surface.