Inertial confinement fusion targets are complex systems designed to allow fine control of temperature and pressure for making precise spherical ice layers of hydrogen isotopes at cryogenic temperatures. We discuss the various technical considerations for a maximum leak rate based on heat load considerations. This maximum flow rate turns out to be $5\times 10^{-6}$ standard cc per second, which can be caused by an orifice less than half a micron in diameter. This makes the identification of the location and resolution of the leak a significant challenge. To illustrate this, we showcase one example of a peculiar failure mode that appeared suddenly but persisted whereby target production yield was severely lowered. Identification of the leak source and the root cause requires very careful analysis of multiple thermomechanical aspects to ensure that the end solution is indeed the right remedy and is robust.