to pull through

from The Collaborative International Dictionary of English v.0.48

Pull \Pull\, v. i.
   To exert one's self in an act or motion of drawing or
   hauling; to tug; as, to pull at a rope.
   [1913 Webster]

   {To pull apart}, to become separated by pulling; as, a rope
      will pull apart.

   {To pull up}, to draw the reins; to stop; to halt.

   {To pull through}, to come successfully to the end of a
      difficult undertaking, a dangerous sickness, or the like.
      [1913 Webster]