The policy on how long to stand behind crowns differs among dentists. There is no standard for that amount of time. There are many things a dentist thinks about in making this decision on how long he feels responsible for them. First, if insurance paid for a portion of the crown, they generally will pay for a new replacement crown after only five years. Thus, many dentists have taken this five year as a minimum goal. But most dentist strive to have their crowns last a lifetime!
A major concern that affects many crowns is any habits that patient may have bruxing (grinding) or clenching their teeth. Both those factors often lessen the life expectancy of porcelain crowns and the underlying teeth. That is something neither the dentist nor the patient has much or any control over.
Other concerns are the oral hygiene habits of the patient. If new decay appears around the crowns and new crowns are then needed, the dentist would have absolutely no responsibility for doing them over. Also, any trauma to the crowns. A fall, a blow to the mouth, biting on very hard objects (usually inadvertently) all can cause crowns to fail.
Some dentists offer no warranty whatsoever after the crown is placed. Others, usually dentists who charge more to cover future breakage or replacement, may cover their crown and bridgework for "a lifetime". However the number of dentists doing that is very small. Some dentists offer a sliding scale. If needing replacement after on year, patient pays 20% After two years, 40%. After three years. 60%. After four years. 80%. After five years, full fee.
Another thing to consider is how long other items you commonly buy are warrantied? How long for your car? Your house? Major appliances? Computer? In general most dentistry lasts for years!
Regarding your problem, was it your dentist's fault your tooth broke? Probably not. He was just doing the best with what he had to work with. I would not expect that he would pay for your entire treatment to be redone. However, if he is generous, he might offer you a reduced fee for redoing the work. On the other hand, if the bridge itself broke, and not just the tooth like you mentioned, then the dentist might consider giving you more consideration.