Well, to increase the voltage [current] by double, an ideal perfect DC converter would need to have double (more for real converters) the current [voltage] supplied to it by the battery. So the battery still supplies the same amount of energy for the same amount of time before dying, it is just in a different form (balanced between voltage and current). You can't make something from nothing as we've established...
but you can make something less from something even more and this is how linear converters work. Linear converters can only step down voltage. WHat they do is burn away the extra "voltage" to provide a reduced voltage. What this means is that if I need 5V@1A from the regulator, but I am supplying 9V to it, it will still draw 1A at the input and burn away the extra 4V as heat (the input and output currents are always the same, ideally in reality a little bit more is drawn to keep the regulator running). If you use a switching converter (step-down in this case) you can extend battery life because a perfect switching converter does not burn off the extra energy as heat. A perfect step-down switching converter only draws an Iin = (Vin/Vout)*Iout. It actually converts the balance of power between current and voltage at the output rather than burning off the extra. So in this case battery life would be extended.
So if your battery voltage is higher than what the circuit is using, you could increase complexity and lifetime by doing that...but not if your battery voltage is lower than your circuit voltage.