At a first approximation, blue LEDs typically list a forward voltage of 3.3 volts, and a pair of AAA cells (at 1.5 volts ea) sums to 3.0 volts.
At a second, better approximation, the voltage range (depending on formulation) is all the way from 2.48 to 3.7 volts. As opposed to, say, red or yellow, which list between 1.7 up to around 2.3 volts.
And this is another one of those wonderful places where what looks like an arbitrary number is actually a window into the physics of the universe. At the simplest level, an LED's forward voltage is defined by the band gap. And the frequency of the photon emitted is a direct product of that band gap. Blue LEDs typically require more voltage because the light they emit is of a higher frequency.
But only at a first approximation. LED physics is a lot more complicated than that. In any case, because this is a photonic effect (as well as a diode junction), an LED isn't like an incandescent bulb. They either light, or they don't. There's no equivalent of the barely-seen glow of a filament on the last dregs of a discharged battery.
So this is the long answer of why a blue LED would make a poor match-up with a pair of AAA cells; theory says the cells would just barely provide the necessary voltage to make the light turn on, and a bare fraction into their lifetime, that voltage would drop too low to work any more.
There is enough wiggle room in these numbers, however, to make experiment worthwhile. I stuck a blue LED in my bench rig (a pair of AAA batteries in a holder and a couple lengths of jumper wire). And four days later, it is still shining.
Why? Well, one factor may be that I'm using rechargeable batteries. They start with a lower voltage, remember, but at least in the Sony "Eneloop" series, they maintain that voltage for a much greater part of their discharge curve. The voltage does not droop significantly until they've reached a good 70% of the total capacity.
Note in passing that the capacity of batteries also changes over discharge rate. When you state a battery has "1500 mAh" you have to specify the typical amperage of the draw. For AAA batteries, that stated amperage is 15ma. Which, fortunately, is within the range of what a single high-brightness LED imposes.
(Incidentally, I just realized I could have made these things with Pirahnha RGB's, and changed color with just a jumper).
Still, the red LED in the prototype is now on six days of continuous use, and showing no signs of dimming either.