Like many 1x18650 lights, the reason the EA4 can only manage short bursts of bright light is thermal rather than battery limitations. A light such as the EA4 can't possibly draw more than three amps (probably less, since it uses four cells). And this is well within the realm of what an Eneloop can produce on a continuous basis. Larger lights like the EA8 and TK41 have both greater thermal mass and more surface area through which to dissipate heat. So they can run at their highest setting until the batteries are drained.
No, not only thermal, though that is also an issue. Cell efficiency is lowered at high current draw due to higher internal losses.