Could be a bad cable a bad charger, etc.
First thing to try put the charger in a plastic bag and put it in the freezer for a while. There is a overheat swicth that sometimes gets stuck in the charger, if that is the problem this should be a fix.
Other wise call ASUS and ask for a RMA to get a new charger.
Buy an new charger and see if it solves the problem, make sure that you purchase it from a retailer that will allow an easy return.
In the mean time to prevent the TF battery from completly going dead turn off the TF and connect it to a standard USB charger. It will take at least 12 or more hours to get a full charge, so be patient.