Should a crack in drywall under the window continue to return after being repaired 4 times by 4 different contractors?

No it shouldn't. Sounds like there is serious stress on the window framing. First check the foundation below the window to see if there are any cracks in the foundation. If there are you may have foundation problems. Although normal settling might still be your problem on a new house, the next place that might cause stress is the window framing. To prevent sagging the top of the window frame should have a 2" x 6" board spanning the oppening. This will direct the roof forces to the sides of the window frame without sagging. A 2" x 8" should be used for long window openings. One way you might check the width of the header board above your window(without tearing out the wall) is with a stud finder. This is a $20 small device that you slide along the wall and lights up when there is wood right behind the wall. Slide it (upside down) from the ceiling down to your window and see where it lights up. Should be four or five inches above the window (allow for the amount you can't check because of the molding around the window. There should also be adequate framing below the window to support the window weight withought sagging. This is typically a doubled 2" x 4" lying so the 4" side is vertical. And it should be supported by studs on the sides and in the middle. All of the problems can be fixed, but sometimes its a bear finding out the exact cause. Good luck.