Kitten dying after 4 days?

Nicah • Scarlett Drew, March 18th 2017💕
So my sister adopted a 13 week old kitten from a shelter in Clarksville TN for her daughter who is two. And they had her for 4 days before she died. They took her to the vet and they said she had to be put down. My sister went back to the shelter to explained what happened and they said she could choose a new cat but all the cats looked sickly like the last. She said that at first she just thought they were lonely and scared but she thinks it's something different. Does anyone have any info about shelters? The kitten was vaccinated and when my sister called to say she was acting weird they said she would be fine, just adjusting but she was slowly dying for the four days...