Can you either post a photo here or email one to Steve@ExoticRainforest.com

The soil should be kept evenly moist as well as keep the plant in moderately bright light. The thing that concerns me is there has been an Anthurium blight running around the globe for some time and your basic description resembles the symptoms. Don't panic since it could easily be something else.

This blight has occurred in the labs of more than a few tissue culture companies and once it is established it cannot be cured. This blight largely affects plants that are known as "ornamental" Anthurium which is likely what you purchased. They just have to destroy all the affected plants so I'd like to show your plant to a couple of experts.

How long after the first plant died before the second plant began to do the same thing?

Other than that you might find help in the link below.

Here is a link that might be useful: Growing Anthurium