Why is Antioch not in communion with Jerusalem? In short, because in 2013 the Jerusalem Patriarchate appointed a bishop in Qatar, an area that has been defined as part of the territory of Antioch since at least the fifth century. According to Orthodox canonical tradition, the proper response to an incursion into universally defined ecclesiastical territory is a break in communion—a step that Antioch took after trying to work things out with Jerusalem for about a year. (See this detailed timeline for a full background.)
Qatar is probably not the first place people think about when they imagine Christianity in the Middle East (if they imagine it at all), and indeed, there is only a single Orthodox parish in the whole country. But Qatar has a long association with Antioch and was the homeland of St. Isaac of Syria (also called Isaac of Nineveh).
The parish in question, located in Doha and largely attended by immigrant and guest workers from a variety of Orthodox cultures, is not really the subject of a “turf war” between Antioch and Jerusalem, though it might seem that way from the outside. The parish was founded in 1997, through the influence of (now retired) American ambassador Patrick Theros (who now serves as something of an ambassador to the US for the Jerusalem Patriarchate), and its first priest was the now-Patriarch Theophilos III of Jerusalem. Though Theophilos was a priest of the Jerusalem Patriarchate, during church services he commemorated the Antiochian metropolitan archbishop of Baghdad, as a sign that he was on Antiochian territory. (This is not a terribly unusual situation. There is, for instance, a Russian parish in Sharjah in the United Arab Emirates whose clergy commemorate the Antiochian bishop.)
The situation—a Jerusalem priest serving in Antioch’s territory—was provisional at best. But there is a reason why no Antiochian clergyman had been assigned to the parish in Qatar: The Qatari government wouldn’t allow it. Qatar is fomenting unrest in Syria, and since the Antiochian church is based in Damascus, Qatar will not issue visas to Antioch’s clergy. It is therefore impossible for Antioch to minister directly to this piece of its territory.