An interesting article has been produced by the WTBTS regarding 'how to end the silent treatment'. The Awake June, 2013 discusses certain issues about partners using this behaviour. The fact is that the silent treatment is used on disfellowshiped JWs and their statements can equally apply to them.
Here are some quotes from the article -
"Retaliation. Some spouses use silence as a form of revenge.
Manipulation. Some use the silent treatment as a means to get what they want.
The first step to ending the silent treatment is to recognize it for what it is—a tactic that, at best, works only short-term.
But is that really how you want to treat someone whom you have vowed to love?"