At this point, I would do all the basic resets for the iPad, starting with clearing the multi task tray (double click the home button, the tray opens at the bottom, hold an icon until it wiggles, then tap the red minus sign on each app in the tray.)
Then, I would shut down the iPad (hold the power button until the red slider comes up, then slide off). Restart and see how that goes.
If that does not correct the issue, I would escalate to a hard reset, and after that, a restore.
If none solve the problem. A trip to an Apple Store might be he next option.