The man's family keeps postponing the wedding date. How should we act?

Ask directly for an explanation and set a clear new date, because an engagement without direction harms your daughter. The delay may be due to money, work or doubts that have not been voiced. The wali (guardian) or a family representative can ask kindly: ‘We would like to know what the obstacle is, so we can find a way together.’ If the problem is the cost of the celebration, suggest a simple akad first. If the answers keep evading the question, discuss with your daughter whether this engagement should continue. Ending an engagement with good manners is better than waiting for years without certainty. See a suitable length of engagement.