Hans Castorp stays seven years because, in the third and last week of his visit, the fever and Dr. Behrens's examination declare him ill. From then on he never decides to leave, and only the war takes him away from there.
The immediate motive is medical. In Chapter IV, a cold leads the head nurse to sell him a thermometer, which reads 37.6. Behrens examines him and concludes that he was, "secretly, one of ours," and that it is not worth returning. The mountain air, the doctor explains, is good against the illness and also for it, because it brings out the latent illness.
But the novel gives a deeper reason, and gives it before the diagnosis. In Chapter II, the narrator explains that Hans Castorp's era did not answer the question "What for?", and that without this answer only a heroic isolation or a very robust vitality allows one to undertake a greater work. He had neither. A young man without direction finds in the sanatorium an entire world, with routine, masters, and passion.
He also never chooses to stay. In Chapter III he refuses to leave so as not to appear a coward; in Chapter VI Uncle James Tienappel goes up to take him away and comes back alone; and in Chapter VII it is the war, and not a decision of his, that returns him to the plain.