The invention provides an electric storage apparatus, a control method thereof, a system for monitoring an electric storage apparatus, and a storage medium, wherein the self charging amount of electric storage apparatus such as a storage battery can be reduced to incapable of starting an engine without an external system. A BMS (13) is configured to switch a state of a relay (12) from a closed state to an open state if a fact that a cell voltage of a cell (C) of an assembled battery (11) is equal to or lower than a power-saving threshold is determined, thereby preventing power consumption of an electric storage device by an electric load. The BMS (13) is further configured to switch a power consumption mode of the BMS (13) from a sleep mode to a deep sleep mode if a fact that the cell voltage is equal to or lower than the power-saving threshold is determined, wherein the BMS (13) in the deep sleep mode consumes less power than the BMS (13) in the sleep mode, thereby preventing power consumption of the assembled battery (11) by the BMS (13).