Rough or patterned surfaces infused with a lubricating liquid display many of the same useful properties as conventional gas-cushioned superhydrophobic surfaces. However, liquid-infused surfaces exhibit a new failure mode: the infused liquid film may drain due to an external shear flow, causing the surface to lose its advantageous properties. We examine shear-driven drainage of liquid-infused surfaces with the goal of understanding and thereby mitigating this failure mode. On patterned surfaces exposed to a known shear stress, we find that a finite length of the surface remains wetted indefinitely, despite the fact that no physical barriers prevent drainage. We develop an analytical model to explain our experimental results, and find that the steady-state retention results from the ability of patterned surfaces to wick wetting liquids, and is thus analogous to capillary rise. We establish the geometric surface parameters governing fluid retention and show how these parameters can describe even random substrate patterns.