We study failure detectors in an asynchronous environment that admits message omission failures. In such environments, processes may fail by crashing, but may also {\em disconnect/} from each other. We adapt Chandra and Toueg's definitions of failure detection completeness and accuracy to the omissions failure model, and define a weak failure detector less than or greater than W(om) that allows any majority of the processes that become connected to reach a Consensus decision, despite any number of transient communication failures in their past. We provide a protocol that solves the Consensus problem in this model whenever a majority of the processes become connected, regardless of past omissions. Moreover, in our protocol it is not necessary to save and repeatedly send all past messages, which makes it more efficient than previous protocols in this model.