What does Juarez mean by the phrase ""the incessant convulsions that the Republic has suffered""?

He meant that, the Mexican Republic has suffered from severe but incessant political instability and violence

Explanation:

This statement is credited to Benito Juarez, the 26th president of Mexico, who held the position between 1858 to 1872, he is identified as a liberal and was regarded as a preeminent symbol of Mexican nationalism and resistance to foreign intervention.

In his view about the Mexican 1824 constitution, he said amongst other things " ... The constitution of 1824 was a compromise between progress and reaction, and that (it was a) seedbed of the incessant convulsions that the Republic has suffered, and that it will still suffer while society does not recover its balance by making effective the equality of rights and duties of all citizens and of all persons who inhabit the national territory, without privileges, without exemptions, without monopolies, and without odious distinctions ..."

Hence, he is referring to the 1824 constitution of Mexico which is the basis for incessant political turmoil, instability and national violence in Mexico at the time.