The zoo was in an unenviable position. Generally, an organization can join in the meme-ing and that's usually the meme's swan song. But given the situation, that wasn't really an option for the zoo.
The meme is both hilarious and offensive, and that's part of why it has managed to last much longer than a meme's usual lifecycle. However, there's a line between making a GIF of Vin Diesel driving next to Harambe at the end of Furious 7 and harassing some communications staffer or intern at a zoo. The latter is unpleasant for someone who probably doesn't deserve the relentless ribbing. Shutting it down might have been the zoo's only option, and that's unfortunate for an organization that lives and dies on donations.
Hopefully, the zoo can rejoin a Harambe-less internet some day, when the next thing comes along. Maybe that thing will be something more deserving of endless ridicule, like Ryan Lochte.