Short Answer: A droopy Monstera is most likely due to under-watering, but it could also be a case of over-watering, bug infestations, a recent transplant or lack of light (even though, yes, they are usually good low-light plants).

Below are some steps and methods to try in diagnosing the problems on why your Monstera is droopy. 

Overwatered Monstera Deliciosa will have a yellow discoloration that starts from the outer edge of the leaves. It will spread inwards until the leaf is fully yellow and die if the watering doesn't decrease. 

Overwatered Monsteras will also look droopy and stems will usually bend downwards due to the saggy leaves. 

Underwatered Monstera Deliciosa seldom kill the plant. Believe it or not, you can stop watering Monstera Deliciosas for a few weeks to a month and the plant will be just a little droopy but not enough to kill the plant. 

Monsteras like to be on the drier side so it's way easier to kill it by overwatering than underwatering.

Positioning

Sometimes you might have done everything under the sun right from watering to fertilizing but your Monstera is is not happy. Try moving your plant around the house to test different lighting. It's sometimes unexplainable that certain plants love certain spots in your house. 

Repotting

Make sure your transplant pot in only a few inches bigger than the one you were using previously. It’s possible that the roots were damaged during transfer. Just pay extra close attention to your Monstera’s needs and it should adjust with time.

Monsteras like to be root bound so don’t be too worried about giving the roots a big pot to grow in. Increase the size of the pot gradually as the roots grow.

This picture shows a very badly root-bound Monstera and needs to be repotted before it gets to this crowded or it would hinder the plant's growth.