Here's a very clear to the point article about the history of Iraqi Christianity.
Not noted is how the history of the Indian Orthodox Church is bound up in the history of the Church in Persia. First of all, as inheritors of the "Syriac" tradition, we have to look at Iraq/Iran as the cradle of our theological tradition. In India, we have relics from both West (Antiochene) and East (Assyria, Persian) Syriac. Moreover:
From the 4th century through the 14th, Iraq had many centers of Christian scholarship and devotion. Apart from Baghdad itself, the Church of the East had metropolitans at Basra, Kirkuk, and Erbil. Jacobite leaders often made their home in Tikrit, which served as the seat of the Maphrianus (Consecrator), head of the Jacobite church throughout the East. Tikrit in modern times gained notoriety as the home of Saddam Hussein and his Sunni Muslim al-Tikriti clan.
Our Catholicos traces his lineage from St. Thomas through this very same Maphrianate mentioned. The idea of 'thrones' is very nuanced, I know, but still we should look at the dying of the Church in Iraq as the loss indeed of a part of our own (Malankara Syrian) heritage.
On top of that, as the fate of this church and the other churches in the Far East indicates, we are by no means guaranteed that a particular church will last forever. Christianity of course, the Body of Christ will forever endure, but we must remain vigilant that our own local and national Churches will not erode and fade away.