Heat sinks with radial and constructal branching microchannel networks with loops are examined numerically. Radial and constructal networks are embedded in disk-shaped heat sinks. Constructal nets with loops are found to be more robust than the radial ones, when one or more channel segments are blocked. Since complex constructal networks would involve problems in manufacturing, constructal channel nets with loops may be a better choice in engineering applications. Networks with loops and without loops are compared. Results show that the constructal nets with loops provide a great advantage when the structure experiences accidental damage in one or more subchannel segments, since the loop assures the continuity of flow. In spite of blockage, the performance of the network has only a small drop considering the increased pressure drop.