I've given this some thought and think that you may have a bad battery... or it could possibly just need to be put on charge while plugged into an electrical outlet and not USB. Some USB ports don't trasmit the amount of power required to correctly charge smartphones.
There's a debate on whether or not you should run down these batteries before charging. My personal experience is it's better to just charge them when you can and avoid draining them below 10-15%. Another hobby of mine is R/C vehicles and I have quite a few LiPo batteries for them... most manufacturers and other R/C enthusiasts are very stern on not draining a LiPo completely down as it can cause damage to the cells that may prevent them from taking a charge. Not to mention the possibility of fire! However this is just how I approach it... this certainly does not mean that I am 100% correct. It is just how I handle these types of batteries and have had pretty good luck with them so far.