They are. Like Avenger said, most of the floor space in the city is vacant. But in spite of the fact that their economy has gone stagnant, there's still a shit-ton of oil money there. It's just not moving around. So, the Sheiks are still building their toys. They're probably hoping that once this recession/depression blows over that business will pick up again.
I think they're in for a shock though. I don't think Dubai is ever going to recover fully. The super-rich are the only ones who can afford to stay there, and the super-rich are fickle motherfuckers. The novelty of Dubai has worn off. They can't downscale to catering to the merely wealthy, and they have no attractions geared to the middle-class.
Dubai is a totally artificial tourist attraction, like Las Vegas. They built a city in a desert where there are no natural draws for tourists. Las Vegas survives because of the party atmosphere that Dubai's cultural laws make almost impossible. Sure, Dubai has a beach, but a beach palls as fast as a tourist sunburns. Other than that, they have...sand. Even the hotels and towers, as extraordinary as they are, can only hold someone's attention for a day or two.
Dubai is fucked. It's probably destined to become the world's most expensive ghost town.