Provided are a method, system, and program for using a heartbeat signal to maintain data consistency for writes to source storage copied to target storage. A copy relationship associates a source storage and target storage pair, wherein writes received at the source storage are transferred to the target storage. A determination is made whether a signal has been received from a system within a receive signal interval. A freeze operation is initiated to cease receiving writes at the source storage from an application in response to determining that the signal has not been received within the receive signal interval. A thaw operation is initiated to continue receiving write operations at the source storage from applications after a lapse of a freeze timeout in response to the freeze operation, wherein after the thaw operation, received writes completed at the source storage are not transferred to the target storage.