You can remove & root all of the stems as new plants. They will root in water or moist (not soggy) soil. Do a search to learn more about coleus cuttings if you would like to try. You can also "save" your plant through winter this way - with cuttings in jars or bottles.

If you have somewhere in the ground to put the root ball, that may save it. If not, try removing it from the pot, replace the dirt, then replant it. It may be too rotted to recover but certainly worth a try.

Thank you, I will try replanting it in the pot with all new soil and also will cut some of stems to try as new plants. Is it the roots that become rotted and that is why the plant has not responded and continues to droop?
Kate

It's hard to say without pics, but that's what I would guess, root rot. If any of the stems are "mushy" they are probably too far gone. Try taking cuttings of firm stems, they should snap like celery.

Just curious about what happened to your coleus?