What causes many endangered species that are now found only in zoos to have very little genetic variation?
The absolute size of the gene pool decreases with the controlled population of species and the genetic diversity decreases.
In a zoo, the population is monitored and controlled. A population of organisms mate with each other and the offspring mate with the former generation and current generation.
Essentially, its members of the same family mating with other family members. As a result the gene pool in each organism can become limited, especially if the zoo did not begin with a large, genetically diverse population.
An analogy is like a monocrop farm with the crops reproducing with with each other.
Zoos in the US that are accredited by the American Zoological Association have breeding plans that they need to form and then consider specifically to prevent a decrease in genetic diversity from happening. You can read more about this here.