In this paper, we investigate the robustness of the 60 GHz connectivity in typical indoor environments by analyzing the outage probability. We define three realistic indoor scenarios which may host the 60 GHz networks in the future and perform simulations with a verified 3D ray tracing tool on them. In the first set of simulations, we show the impact of access unit position on the connectivity. In the next step, we show that the outage probability of the 60 GHz network linearly increases with the obstacle density and this increase is found to be sharper for the certain positions of the access point. In the last step, we demonstrate the direct effect of the reflective surface availability on the connectivity. A 60 GHz indoor network relying solely on the reflections in the absence of line-of-sight path is very vulnerable to outages even in moderately populated indoor environments.