We study the effect of link failures on the solvability of problems in asynchronous systems that are subject to process crashes: given a problem that can be solved in a system with process crashes and reliable links, is the problem solvable even if links are lossy? We answer this question for two types of lossy links, and show that the answer depends on the maximum number of processes that may crash and the nature of the problem to be solved. In particular, we prove that the answer is positive if fewer than half of the processes may crash or if the problem specification does not refer to the state of processes that crash. However, in general, the answer is negative even if each link can loose only a finite number of messages.