The changes of temperature, salinity and ocean current in underwater environment, have adverse effects on the communication range of sensors, and make them become temporary failure. These temporarily misbehaving sensors are called dumb nodes. In this paper, an energy-efficient connectivity re-establishment (EECR) scheme is proposed. It can reconstruct the topology of underwater acoustic sensor networks (UASNs) with the existing of dumb nodes. Due to the dynamic of underwater environment, the generation and recovery of dumb nodes also change dynamically, resulting in intermittent interruption of network topology. Therefore, a multi-band transmission mode for dumb nodes is designed firstly. It ensures that the current stored data of dumb nodes can be sent out in time. Subsequently, a connectivity re-establishment scheme of sub-nodes is designed. The topology reconstruction is adaptively implemented by changing the current transmission path. This scheme does't need to arrange the sleep nodes in advance. So it can reduce the message expenses and energy consumption greatly. Simulation results show that the proposed method has better network performance under the same conditions than the classical algorithms named LETC and A1. What's more, our method has a higher network throughput rate when the nodes' dumb behavior has a shorter duration.