Just as a point of reference: Mr. Haskell has spasmodic dysphonia, the same condition as longtime NPR host Diane Rehm.
There is no law that a company must continue to employ people who can't perform the work to whatever standard the company sets. For example, if an employee had a stroke and could no longer speak clearly, a radio station would be able to let that person go.
Accommodations can be required for disabilities that don't affect the employee's productivity. As an example, if an employee used certain medications requiring refrigeration, an employer might be expected to provide a refrigerator at that employee's usual place of work.