This is a topic that not many people think about. While it isn't a big factor in the grand scheme of things, some companies do provide some coverage for these diets. These diets are usually more expensive than your pet's usual diet.
What is a prescription diet? It is a diet usually available only from your veterinarian for a specific medical condition. There are several companies that manufacture prescription diets like Hills, Iams, Purina, and Royal Canin. Examples of these diets are K/D for kidney failure, S/D and S/O for dissolution of struvite urinary stones, H/D for heart failure, etc. Studies have shown that some of these diets prolong a pet's life while also providing a better quality of life.
The reasoning for not covering the diets is that if your MD recommended a low salt diet or low-fat diet, you would alter what you eat, but your health insurance policy wouldn't pay for it.
Diets for weight loss generally aren't covered.
Generally, diets to dissolve stones are covered while the patient is symptomatic, but they don't cover a maintenance diet after the stones are dissolved.
The decision to provide long-term coverage for prescription diets is decided on a case by case basis depending on the condition being treated (whether it has resolved or is on-going) and in consultation with the veterinarian recommending the diet.
Update: See podcast episode about this topic.