For a total drain of 120mA from your 6 LEDs, the total drain from the battery for 2500, 4-sec. triggers would be .12*2500*4 = 1200 amp-sec or 1200/3600 = .33 Ah.
An alkaline AAA battery has about 1 AH of capacity at 1V end voltage, so the battery would be drained of about 1/3 its capacity for your 2500 pulses, at which point the battery voltage will likely be about 1.3V.
That will cause some dimming of the LEDs with a resistor to control the current, but may not be that objectionable.