Originally Posted by
Qualia
As others have said, the Draenei joined the Alliance partly because the Night Elf helped them, and partly because they were inspired by the tales of the Alliance fight against the Legion while being able to sense the Alliance's great courage ("Sensing the great courage in the Alliance, Velen and his followers pledged themselves to this noble faction"). Since then, the Draenei and the Alliance have gone through thick and thin, wars over wars - at certain time, the bond between them weren't enough and the Draenei were almost going to fly off (in Velen's short story), but in the end, they stuck together. The Alliance races are pretty friendly and supportive to each other, so I assume the Draenei doesn't really have anything against being part of the faction either. Their bond was again strengthened when the Alliance helped the Draenei to reclaim their former holdings from the Legion. So, to sum it up, they are still part of the Alliance because (1) they admired the courage of the members of the Alliance, (2) the relationship between Alliance races were pretty good - which led to strong bonds, bonds that can't be broken simply because they are in danger (in fact, given that Sylvanas Horde is aiming to take over entire Kalimdor, there are more reasons for them to stick with allies).
Secondly, they actually do participate in the war, even though it might not be as clear as it could be. The reason why they haven't taken a bigger role is because their resources were already depleted from the battle in "Legion" ("The night elves and the draenei were the only Alliance bastions on the continent who could offer a swift counter to a Horde incursion into Silithus, and the draenei’s resources had been depleted during the war against the Legion"). However, some of the Draenei - even though they are in danger of being invaded by the Horde themselves, still traveled to help in battle for Teldrassil (quoting "Elegy", "The draenei were hardly in a position to assist the beleaguered night elves, though some brave souls had traveled to do so"). Now, they are providing a place for NE refugee and participating in the Battle for Lordaeron, while Velen participated in meeting with other leaders of the Alliance to discuss strategy, like they did before the burning of Teldrassil.
All in all, they are doing something. They just couldn't do much because of lore handicap (wouldn't make much of a war if the Draenei just fly around and light beam Horde's force from the orbit, would it?), but they are trying to contribute as much as they can.