Prolonging battery pack life
1 Depletion below the low-voltage threshold (2.4 to 2.8 V/cell, depending on chemistry) results in a dead battery which does not even appear to charge because the protection circuit (a type of electronic fuse) disables it. This can be reversed in many modern batteries, especially single-cell ones, by applying a charging voltage for long enough to make the cell voltage rise above the low-voltage threshold; however this behaviour varies by manufacturer.
2 Lithium-ion batteries should be kept cool; they may be stored in a refrigerator.
3 The rate of degradation of Lithium-ion batteries is strongly temperature-dependent; they degrade much faster if stored or used at higher temperatures
Yeah, with the DS battery it's better not to have it die or get close to being completely depleted, while with another type of batteries it actually helps having it go dead and then charging it. There have been threads about this in the past where it was explained in more detail why it helps not to let the DS battery die in order to prolong its lifespan (or rather not to shorten it).