There is a cut off after it's fully charge and it won't re-charge until the battery is below certain level (most probably below 85%).

If I'm not wrong, this is actually to protect from over-charging your battery.

As with Li-Ion and Li-Poly technology, you should always keep your battery charged, never let it drain completely as compared to older battery types. If you let the battery drain completely, you risk damaging the battery or shorten the lifespan of the battery.

i learned this the hard way with my Motorola MPX200, I left till the phone turn off itself almost everytime before re-charge and the battery died on me right after 6 months, which is the warranty period for the battery. After that, did some research and found out that I shouldn't have drain the battery.

Frequent usage and top up will make the battery more efficient too. This is also from my experience with my PSP when I played multiplayer games with my friend.Both of us have full bar or at least 90% battery, and his PSP died half way while my PSP still have 2 bar left. After some talk, found out he always drained off his PSP battery.
You can also read some other examples from the web, someone did a test on N95 with different type of charging cycle.