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Does the monthly rate of expenditures on cases rise faster the longer the case lasts?

At the Ninth Annual SuperConference, David Grumbine, Senior Counsel, Dispute Resolution Group, of Whirlpool Corporation spoke about best practices for working with outside counsel. He stated: “Work expands the longer a case is open and the more money it costs.”

A trivial point, if Grumbine was merely saying that all things being equal, the longer a case drags on the more it costs a company in fees and disbursements.

But the implication seems to be that the increase in costs is not linear over time, steadily adding up, but instead accelerates. Is it common that that plaintiff’s counsel invests more and more as a case continues, so clients incur higher burn rates each month (See my post of May 3, 2009: burn rates of outside counsel with 6 references; and .). Stated more technically, as cycle times length does the second derivative of costs increase (See my post of April 24, 2009 #3: explanation of the rate of change changing.)?