One thing you should keep in mind is that new batteries need cycling to keep their charge for any length of time. This means you should charge it fully, then let it drain fully three times in a row before the battery keeps its charge for longer.
That said, the battery in the Cinera doesn't seem to keep its charge for very long. I think I get twenty minutes on one charge. For longer periods, it's best to leave the Cinera connected to the power adapter while using it. As Ron said, make sure to connect via the bottom USB port. Alternately, you can also connect a portable battery pack.
If, as you describe, Cinera shuts down even when it is connected to the power adapter, this very much suggests that your USB cable is faulty. A friend of mine who got his Cinera also was having problems with his Cinera shutting down even when connected to the power adapter and he eventually found the problem was corrected by switching to another USB cable. Try that and let us know if it helps.