What are "concentric eyewall cycles" (or "eyewall replacement cycles") and why do they cause a hurricane's maximum winds to weaken?

"Concentric eyewall cycles" (or "eyewall replacement cycle" ) naturally occur in intense tropical cyclones, major hurricanes (winds: 50 m/s, 100 kt, 115 mph) or Catories 3, 4, and 5 on the Saffir-Simpson scale. As tropical cyclones reach this threshold of intensity, they usually - but not always - have an eyewall and radius of maximum winds that contract to a very small size, around 10 to 25 km [5 to 15 mi]. At this point, some of the outer rainbands may organize into an outer …

…eyewall completely replaced the original one the hurricane reintensified. Another example is Hurricane Allen (1980) which went through repeated eyewall replacement cycles -- going from Categrory 5 to Category 3 status several times. It was the discovery of concentric eyewall cycles that was partially responsible for the end of the U.S. Governements's hurricane modification experiment Project STORMFURY, since what the scientists had hoped to produce through seeding was happening frequently as a natural part of hurricane dynamics.