the black colocasias can be grown as aquatic plants, they like LOTS of water, especially in the heat, so my simple guess, without knowing other details, is that it needs more water - what type of soil is it planted in? you can tie to stakes but that really should not be necessary with these plants

mine did the exact same thing. i guessed that it was too top heavy b/c they are about 5 feet tall. did you ever figure out what to do about this?

I had three plantings - all died. great healthy plants planted in extreemly ideal situation, just like the Regular green elephant ears. I added plenty of compost and burmed up the soil making a 6 inch deep pool when watered. I kept the soil very moist to wet, knowing what they fancy.
*One thing..... these were in full sun. Now I have read that this is fine if you water well, as I did.

I am now convinced this is not true I beleive the Black Magic cannot tolerate full sun.

Case in point:
Same location, soil and watering for my green Elephant ears in a spot next to the Black magic, growing tremendously. Knowing that there is some sort of issue with the blackies, I purchased an "insurance" Greenie some 5 weeks back, and potted it up in a large container. When My last Black Magic died (took just 2 days, when it started to go) I replaced it with the Green Elephant Ears and it is now flurishing , so fortunately I do not have a hole in my garden.