[Avodah] Machlokes in Mishnayos, why?

[Marty Bluke via Avodah]

> By "in existence," the Rambam means when it functioned properly. R'
> Yitzchak Isaac HaLevy in his work, Doros HaRishonim develops the sources
> that there were periods of persecution during which the Beis Din Gadol
> could not operate normally, including the time when Beis Shammai and
> Beis Hillel were unable to unite.

The the second Beis Hamikdash lasted 420 years. Was there no time during
those years that the Sanhedrin functioned normally? While there may have
been disruptions there were certainly times when it did function and if so,
why didn't they decide all of the machlokes that had arisen like the Rambam
says?