According to the Holy and Scared canons of the Orthodox Church, the monks are obligated to cease commemoration of a Bishop or Patriarch when his teachings are in direct conflict with what the Orthodox Church teaches.  After seeing many documented instances, in writing, of the Patriarch acting and teaching in direct conflict with the teachings of the Orthodox church, the monks ceased commemoration of the Patriarch of Constantinople as they were obligated to do.

The proper procedure within the church is to call for an ecumenical synod for clarification of the dispute, not a local synod controlled by the bishop in dispute.  It is not the procedure of the church to call the police to enforce a blockade of food, water and medicine to the monks with whom you disagree.

Here is what the canons of the Church say on this: "... So that if any presbyter or bishop or metropolitan dares to secede from communion with his own patriarch and does not mention his name as is ordered and appointed in the divine mystagogy, but before a synodical arraignment and his [the patriarch's] full condemnation, he creates a schism, the Holy Synod has decreed that this person be alienated from every priestly function, if only he be proven to have transgressed in this. These rules, therefore, have been sealed and ordered concerning those who on the pretext of some accusations against their own presidents stand apart, creating a schism and severing the unity of the Church. But as for those who on account of some heresy condemned by Holy Synods or Fathers sever themselves from communion with their president, that is, because he publicly preaches heresy and with bared head teaches it in the Church, such persons as these not only are not subject to canonical penalty for walling themselves off from communion with the so-called bishop before synodical clarification, but they shall be deemed worthy of due honor among the Orthodox. For not bishops, but false bishops and false teachers have they condemned, and they have not fragmented the Church's unity with schism, but from schisms and divisions have they earnestly sought to deliver the Church" (Canon XV of the so-called First-Second Council).