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.
2018 (President Donald Trump): January 20 to January 23 - 3 days
2018 (President Donald Trump): February 9 – 1 day.
2013 (President Barack Obama): October 1 to October. 17 - 16 days
1995-1996 (President Bill Clinton): December 16, 1995, to January 6, 1996, - 21 days
1995 (President Bill Clinton): Nov. 14 to 19 - 5 days
1990 (President George H.W. Bush): October 5 to 9 - 3 days
1987 (President Ronald Reagan): December 18 to December 20 - 1 day
1986 (President Ronald Reagan): October 16 to October 18 - 1 day
1984 (President Ronald Reagan): October 3 to October 5 - 1 day
1984 (President Ronald Reagan): September 30 to October 3 - 2 days
1983 (President Ronald Reagan): November 10 to November 14 - 3 days
1982 (President Ronald Reagan): December 17 to December 21 - 3 days
1982 (President Ronald Reagan): September 30 to October 2 - 1 day
1981 (President Ronald Reagan): November 20 to November 23 - 2 days
1979 (President Jimmy Carter): September 30 to October 12 - 11 days
1978 (President Jimmy Carter): September 30 to October 18 18 days
1977 (President Jimmy Carter): November 30 to December 9 - 8 days
1977 (President Jimmy Carter): October 31 to November 9 - 8 days
1977 (President Jimmy Carter): September 30 to October 13 - 12 days
1976 (President Gerald Ford): September 30 to October 11 - 10 days