AA cell for low power embedded system -Debugging help needed
As a battery ages its internal resistance increases. Therefore, measuring the voltage on an 'idle' battery (i.e. 0 current) will not always yield the same as it does when current is actually drawn from the battery.

If you have 'modules consuming current in pulses' it may well be the case that, during those pulses, the battery's voltage will drop below its 'idle voltage' significantly.

Use an oscilloscope to measure the actual voltage during a pulse.

You may also want to put a capacitor in parallel to the battery. This decreases the overall impedance of your power source for short pulses significantly and will almost always yield a much longer usable time for any battery being used pulsed.

To get a rough (optimistic) estimation of a battery's response to a current pulse, one may measure the voltage during a somewhat 'prolonged' pulse of the same current. - Defining 'prolonged' here is up to the reader, but the point actually is: If a battery's voltage drops below a certain level under constant (current) load I, then it probably will do (even more) so for pulsed loads of the same current I.

If you know that your pulses are 1A max., just put a 1A constant current load (read: resistor) across the battery and take a voltage reading while the current flows. This will definitely reveal a dead battery better than its idle voltage.