(condensed from Ein Ayah, Shabbat 1:72)

Gemara: Hillel, Shimon, Gamliel, and Shimon held the presidency of the Sanhedrin for 100 years during the time of the Temple.

Ein Ayah: Consistency in the path of morality makes a great positive impact in the paths of Torah and of life. When the nation takes a set, paved path over a long period of time, it enables it to persevere long, tumultuous times of troubles. For this reason, Divine Providence arranged that for a long period before the destruction of the Temple and the nation’s dispersion, one exalted family would hold the post of the nesiut (presidium) uninterrupted. These leaders, with a common genealogy, caused the nation’s moral approach to follow one path for several generations. This is because the familial commonality had a unifying effect, regarding attributes, opinions, and even approaches to the study of Torah and halacha. Certainly joint lineage causes similarity in the Rabbinical injunctions that the nesi’im institute regarding national life of Torah day-to-day matters.
The transfer of the nesiut between dynasties could weaken the extent to which the nesi’im’s teachings are entrenched in the heart of the nation, for the educational approach of one counters that of the other. Under such circumstances, the storminess of exile could uproot the holy things that had been planted and guarded as it "grew in the orchard" for generations. That is why Divine Providence, which protects Israel, decreed a consistent Torah leadership (i.e., the chain of nesi’im) over a long dynasty (100 years of Hillel, Shimon, Gamliel, and Shimon), enabling a spirit of sanctity to be established and entrenched through consistency. This took place during the time of the Temple, which helped ensure that the nesiut was fully effective. The resulting impact continued even after the Temple’s destruction, during the course of the dynasty. The dynasty will return (Hillel was also of Davidic decent) with Hashem’s kindness with the kingdom of Yishai’s descendants. That family maintains leadership through Divine Providence for eternity as befits one nation in the Land – "My servant, David, will be nasi for them forever" (Yechezkel 37:25).