You seem surprised.
I don't see why you should be surprised.
As the battery discharges, its voltage will drop below 6V and its output impedance will increase.
You circuit is not working properly because the input impedance is too high and the voltage is too low.
The NCP551 has a dropout voltage of 220mV which means that it stops regulating when the input voltage drops below 5.2V.
Use a fresh set of batteries and the problem should go away.
Unfortunately the voltage will drop below 5.22V when the batteries still has lots of charge left., as a general rule of thumb, you should design circuits to work until the battery voltage drops below 1V per cell., for longer battery life, use five or six AA cells in series.