Here is the official policy from Marriott Rewards Terms and Conditions:
"An account may be closed at Marriott's discretion if no points are accrued during a 24-month period. All points in the account will be forfeited at that time."
http://www.marriott.com/rewards/terms/default.mi
My anecdote is I have had a Marriott rewards account for about 10 years. I had points for years from 2000 to 2003. I don't think I stayed at a Marriott for several years and then redeemed my points for a PointSaver award in Albany NY a couple of years ago.
The hotel upgraded me to the top floor with a preferred view.
I don't think they close accounts too frequently.