It has been my experience that the degausser will not activate every time you turn on the TV if you don't give it some time to cool down. The degausser has to have quite a current flow to make a large enough magnetic field to degauss, and heat is definitely a problem.
What is dust? Is it something that magnetizes only in the presence of a discrete Sony TV ON command?
This is still a mystery. Don't tie dusting to the problem.
A good answer is easier with a clear question giving the make and model of everything. "The biggest problem in communication is the illusion that it has taken place." -- G. “Bernie” Shaw