It's been done, and usually involves at least one of the films bombing. November 2011 had 3 within a month, and Arthur Christmas was a huge bomb. March 2011 had 3 within a month, and Mars Needs Moms was an epic disaster. Granted, those 2 were probably destined to fail anyway, but I don't think many expected them to fail that hard.
It's really stupid to schedule 3 of the same demo movies in a month, unless you're dealing with 4 quadrant stuff.