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Blue Loctite will not work, same with the red formula, these thread adhesives require heat to remove them, and in this case the muffler gets hot. Follow Hondas oem hardware and torque it to specs. (it most likely was not tightened all the way to begin with), Also, before you begin repairs, inspect the threads and make sure the are good.Bummer! You might want to add some Blue Loctite to the new nut when you replace it.
I use a lot of loctite (both Blue and Red) on most of my off-road toys, never with any ill effects YMMV
I'm sure cost is not the issue..... Honda is known for doing it right.