Marine buoys aid in the battle against Illegal, Unreported and Unregulated (IUU) fishing by detecting fishing vessels in their vicinity. Marine buoys, however, may be disrupted by natural causes and buoy vandalism. In this paper, we formulate marine buoy placement as a clustering problem, and propose dropout k-means and dropout k-median to improve placement robustness to buoy disruption. We simulated the passage of ships in the Gabonese waters near West Africa using historical Automatic Identification System (AIS) data, then compared the ship detection probability of dropout k-means to classic k-means and dropout k-median to classic k-median. With 5 buoys, the buoy arrangement computed by classic k-means, dropout k-means, classic k-median and dropout k-median have ship detection probabilities of 38%, 45%, 48% and 52%.