Why shouldn't lithium batteries be discharged below 50%?
There are two main effects that cause damage to a Li-ion battery due to "deep cycling":


During the charge/discharge cycle, lithium ions are intercalated within the electrodes. This causes physical stress to the electrode material and spalling of their coatings. Deeper discharge causes increased stress. This effect is made worse with the temperature range from heavy current use as in a laptop.
Lithium metal may accumulate on the anode, taking it out of play. This effect may be due more to over-charging than to deep-discharge, though.