For Cilicia to survive up to the early Modern Period would require several lucky breaks for itself and its allies. To much past 1500 would require something more significant.
Given its size and religion, Cilicia can only survive and prosper in alliance with a non-Muslim power. The most obvious candidates were its patrons and occasional rivals, the Byzantine Empire and the Crusader states. This would probably entail some loss of independence, but the kingdom would be unlikely to disappear as a result of the actions of either power.
The Mongols, under of the Ilkhanate or the empire of Timurid are another candidate, though I would consider them to be a more remote possibility. Unless the Mongols manage to penetrate Egypt inflict the same degree of destruction to Cairo and the canals as they did to Baghdad and modern day Iraq, the Mamluks or another Muslim power will arise and attempt to expand towards the north, even if they are delayed by a generation.
A Byzantine Empire that somehow managed to avoid the disaster of the Fourth Crusade and the Latin Empire would be apt to maintain a Christian power in Anatolia. Though the Armenians would probably lose ground in Syria, they would be unlikely to be completely overthrown as long as the Byzantines remain capable of projecting power into southeastern Anatolia.
The survival of the Crusader states on the mainland of the Levant would effectively block any attempt to conquer Cicilia from the South. The survival of Edesssa would protect Cicilia from invasion from the south or east. The survival of the Principality of Antioch or the Kingdom of Jerusalem would be immensely helpful as well.