to All Things Plants!
I don't know a thing about the Monkey Puzzle Tree (Araucaria araucana)
only what I read when googling. I learned that it's apparently a relatively disease free tree, requires a fair amount of sun, needs excellent drainage with neither extremely wet or dry soils and it also does not like it's roots disturbed. Is your tree planted in-ground or is it a young container plant? I wonder if perhaps the issue with your tree is originating from the roots? If the plants roots are staying too wet they may be rotting, which in turn will cause the branches to die.
Hopefully someone more familiar with this interesting tree will pop in with suggestions and advice.