Although a related question is also,
If it should happen (thermodynamically speaking), why doesn't it?
Meaning: clearly, a battery should self-discharge, but the rate is the important factor here. How fast does it react, with or without an external load, and why?
If you put aluminum foil in strong base (NaOH / KOH in H2O), no matter how much voltage you superimpose between the two, it reacts spontaneously. This is a kinetically favorable reaction. The reaction does develop voltage all its own, but not nearly as much as you would hope, and it can't be retarded or even reversed by applied voltage alone.
The nice thing about zinc under similar conditions (which is what's used in alkaline cells, but similar reasons follow for all types), is the reaction kinetics are low: it tends not to proceed, just sitting there; but it develops a voltage, and when you short that out, it's enough to overcome the kinetic barrier and the reaction proceeds. Presumably, that should suggest that all cells which don't rapidly self-discharge should necessarily experience a terminal voltage drop in use; and the amount of drop is proportional to rate (effectively: how much voltage drop you're "paying" to "bribe" the kinetics into moving) and self-discharge (which might simply be seen as a Norton current source, where the self-discharge current is as large as the load current). This is certainly apparent for several main types (alkaline, NiMH, etc.), but... doesn't seem to follow for others (Li ion, poly?). Differences in chemistry probably dominate as always, or this could simply be an incorrect analysis.
Tim