Why do my potted elephant ears look bad after heavy rains?

The plant is probably waterlogged. University of Memphis Director of Landscape Joellen Dimond suggests checking the drainage. Make sure there is a hole in the bottom of the pot and that the hole is actually draining water. Often, if the pot is set on the ground, the ground blocks the drainage hole.

Related Videos:
Container Flower Garden
Building a Self-Watering Houseplant Pot
Repotting Houseplants

Related Resources:
Container Drainage Options 
Container gardening for small spaces: big beauty in tiny places