There are 2 possible problems. The first is that someone tried to plug in the USB charger improperly and bent the little metal tab in the playbook and though the USB charger is going into the port it is not properly connected and is not charging. Look at it closely and if the tab is bent downward, take a little piece of plastic and pry it straight, then plug the USB charger in.
The other problem is the Playbook gets too low on power and will not take a charge. The playbook charging circuit is software controlled. If the power is too low the software won't run to charge the playbook, When you first plug a charger into a Playbook it takes a charge for about 10-15 seconds then shuts down expecting the Playbook software to take over the charging process. It the Playbook power is too low, it can't run the software. The solution is to "stack" charge it. The is the process of stacking a bunch of little 10 second charges together to get enough power for the Playbook to run the charging circuit software. To do this, plug your USB charger into the Playbook making sure it is properly aligned. Then at the wall outlet, plug in for 10-15 seconds, unplug, plug in for 10-15 seconds, unplug, and keep repeating the process for 50-100 times until you have "stacked" up enough power for the Playbook to charge itself.
Good Luck