In a previous yarn university post I discussed the different types of yarn fibers and described their drape.  I think it is important to talk about the difference between drape and droop.

Drape takes advantage of natural fiber and fabric properties to make something look good.  Droop is when the fibers do something undesired and make it look like crap.

Wedding dresses drape, flour sacks droop.

Quality cotton and wool yarns will drape and retain their shape.   Cheap yarns and unfortunately acrylics have the tendency to droop.  If you are going to spend hours and hours on a project do what you can to make a quality finished project.  Pick the correct yarns for the situation and avoid a droop disaster.