Loss of power shouldn't cause lockout but a flickering failure might upset things. Normally a loss of power should be interpreted as an end of demand condition with retry on power restoration. Without knowing exactly which model of Bentone control box you have I can't be more specific. Are there any numbers or type labels such as TF801 for example? That would indicate a rebadged Satronic control.
Typical alarm display is the reset button lights up but often a repeater light is mounted on the front of the boiler.