This paper analyzes the downlink performance of ultra-dense networks with elevated base stations (BSs). We consider a general dual-slope pathloss model with distance-dependent probability of line-of-sight (LOS) transmission between BSs and receivers. Specifically, we consider the scenario where each link may be obstructed by randomly placed buildings. Using tools from stochastic geometry, we show that both coverage probability and area spectral efficiency decay to zero as the BS density grows large. Interestingly, we show that the BS height alone has a detrimental effect on the system performance even when the standard single-slope pathloss model is adopted.