General consensus is that batteries claiming to be 3.7v 3000mAh are misrepresenting themselves. I can't find it at the moment, but there was a discussion about this a little while ago, and the general idea was that it's better to stick with what we know works. As to how they started to fail, unfortunately it does happen at times, but have you followed the care for Li-Ion tips?
This is true, but it depends on the size of the cell. A 14500 size claiming to run 3000 mah is clearly not going to provide that type of runtime, but 26650 certainly can run that, if not more.