The shutdown of '96 was remembered as a key issue that drove voters to the polls and cost the Republicans a chance to unseat Clinton for a second term. After that, they lost their taste for it during the remainder of his Presidency.
It may have continued from 2001 onward, but September 11 caused massive realignment in political strategy for years; anyone seen as causing the government's basic functions to stumble while terrorists threatened America would have suffered a colossal political black-eye.
I couldn't guess off the top of my head why 2013 became the year Congressional leadership decided this was a game worth playing again.
