So did this issue just recently occur? If you have taken good care of the device then there are 3 possible issues.
One- your charger cable is faulty. This is easy to check, provided you have another cable/charger. I recently bought a new charger & cable for my wife's Sensation 4g and within a week it no longer worked. The usb cable was the cause.
Two- The battery is faulty. This can happen from time to time, although it is rare. This is also an easy thing to have fixed and will be covered under the manufacturer warranty.
Three- the handset is faulty. If you only recently experienced this issue it may be difficult for you to get this fixed under warranty (since you don't have the protection plan) unless you have taken great care of the device. But it's worth a shot.