Hi jourdy288
The most common thing to kill a cory is a bacterial infection and this must always be considered when a newly added one dies. Do you have more of them in the tank?
Bacterial infections can spread easily, so be prepared to do extra water changes and medicate if your fish continue to have problems.
There are always likely to be some harmful bacteria in a tank, but it's usually only when a fish is stressed that it weakens and becomes sick. This is often the result of such things as overfeeding, overcrowding, high nitrates or nitrites, rapid temperature rises, low oxygen level in the water. Exposure to these conditions can happen during shipping and while in the lfs too, as well as in your home.
Make sure your bottom is well vacuumed and that they aren't being over fed. If the temperature is above 75 degrees F., lower it a bit. You might also want to raise the oxygen level by adding an airstone to cause more surface movement. These things will make the environment less hospitable for the bacteria.
If you had your country of origin listed in your profile I would try to suggest a medication that would help. Perhaps you should ask what your lfs recommends.