The idea that you need to periodically fully discharge a Li-ion battery is one of those myths that is endlessly repeated without checking to see if it's actually true. As Li-ion batteries don't suffer from the "memory effect" of older battery technologies, it's just nonsense. What's more, as the charge-discharge cycle is what largely determines the life of a Li-ion battery, deliberately discharging it simply so that you can recharge it, is likely to shorten its life - and discharging it below a certain level will prevent you from ever recharging it with a standard charger.
You might like to read points 3 and 4 here:-
http://www.techrepublic.com/blog/five-apps/five-tips-for-extending-lithium-ion-battery-life/289