The Jewish state has not been continuous.
The Roman state, in part, has been in continous operation for 2,770 years. It still continues in the form of the Vatican and Catholic church. In Roman society religion was a state function and its offices held by state officials. When Constantine made Christianity the state religion he basically moved out the old gods for a new one. Christians filled the pre-existing state offices, which became the Catholic Church.
The Roman state, in part, has been in continous operation for 2,770 years.
Someone has ruled over Rome since it started, usually, but not always in Rome (Avignon). Constantinople had the better case as the successor State of Rome until 1453, and I would put a claim for the Vatican on part with the Russian claim to be the third Rome.
Continuity isn’t necessary for a successful insurrection—indeed, an interruption of continuity is generally a prerequisite.