Semiconductor memory devices are provided that include a nonvolatile memory that has a plurality of memory cells and a memory controller that is configured to control at least some of the operations of the nonvolatile memory. The memory controller include an error correction unit. Moreover, the memory controller is configured to determine whether a read failure that occurs during a read operation of a first of the plurality of memory cells is due to charge leakage based at least in part on an output of the error correction unit. Related methods are also disclosed.