Some cheap batteries are junk from day one. Another possibility is that there is some drain when the battery is in the TW. Take it out, trickle charge for 24 hours, then test voltage every 6 to 10 hours for two days. If it's still good, there is some drain to chase down. This is somewhat unusual in an unmodified TW, as there is nothing electronic to power when off.
If it's a lead/acid, test each cell with a hygrometer. Most likely, it's a bad battery.....it's real easy to fry a new battery by charging at too high a rate. Lot's of battery threads here.