A disconnection time acquisition system includes a response requesting circuit, a response determining circuit, a response circuit, a time storage circuit, and a time management circuit. The response determining circuit, in a network server, determines whether or not a response signal in response to a response request signal is received. The response circuit, in an electronic device, replies the response signal in response to the response request signal to the network server. The time storage circuit, in the network server, stores a time without the response signal when the response signal in response to the response request signal is not received. The time management circuit manages the time without the response signal as a disconnection time at which a power supply of the electronic device is disconnected when the power supply of the electronic device is turned on.