Let's read about LiOn batteries at Battery U.
" A lithium-ion battery provides 300-500 discharge/charge cycles. The battery prefers a partial rather than a full discharge. Frequent full discharges should be avoided when possible. Instead, charge the battery more often or use a larger battery. There is no concern of memory when applying unscheduled charges. "
It appears to dispute what you heard.
I heard from previous podcast that recharging mp3 player's battery full will shorten the life spand of the battery. At the same time I have heard people say that you should always fully discharge the battery before recharging. So what it is? How to prolong my mp3 players battery life?