Why are MBA programs closing in the United States?
Demand is counter-cyclical.  During recessions, demand rises as people seek additional training, hoping to prepare for new careers.  But US unemployment is currently at only 3.6%.  We haven't seen unemployment that low in decades, so people are not feeling the pressure to seek additional training for new careers.

Here are some references that describe this counter-cyclical behavior of applications to graduate school.

Ilana Kowarski, "Fewer People Are Applying to U.S. Business Schools", US News, Nov 5, 2018


  From a U.S. domestic prospective, historically, U.S. business school
  application volume has run countercyclical to the economy," Basye
  wrote in an email. "In times of higher unemployment or job loss,
  people often go back to school. In times of full employment or high
  GDP growth – like right now – opportunity costs are higher to leave a
  job and return to school.


Jade Scipioni, "Harvard, Stanford, other top MBA schools see applications drop", Fox Business, October 1, 2018


  Sangeet Chowfla, president and CEO at GMAC, notes that historically
  business school application volume have often run counter cyclical to
  current economic trends and indicators. And the current low
  unemployment rate means “young professionals have an increased
  opportunity cost of leaving their jobs in pursuit of an advanced
  degree,” Chowfla said.


Wendi Go, "Is Enrollment into Graduate School Affected by the Business Cycle?", Department of Economics, Stanford, May 11, 2009


  The findings show that the effect of the business cycle on First-time
  First-professional enrollment follows a relatively consistent
  counter-cyclical pattern. More specifically, a 1% increase in
  employment growth is associated with a 4.09% decrease in enrollment,
  while a 1% increase in GDP growth corresponds to a 2.04% decrease in
  First-time First-professional enrollment. Finally, 1% increases in
  personal income growth and personal disposable income growth are
  associated with 1.68% and 1.30% decreases in First-time
  First-professional enrollment respectively.


Srikant Datar, David A. Garvin, Patrick G. Cullen, "Rethinking the MBA: Business Education at a Crossroads", Harvard Business Press, April 22, 2010


  Because MBA programs are often viewed by young people, especially
  those with few other career options, as a safe harbor for weathering
  economic storms, business school applications have historically been
  countercyclical.