I answered this previously saying to try using the OEM charger, but mine just started doing it again, but I don't have the OEM charger anymore. No other charger worked, but I fixed the issue doing this:
1. Pull back cover off with spudger. http://www.techrepublic.com/blog/cracking-open/galaxy-tab-2-70-teardown-reveals-efficient-hardware-layout-and-replaceable-battery/
2. Unplug battery. It's the connector one with red and black wires.
3. Press the power button, and hold for 10 seconds. Use your spudger or fingernail.
4. Plug battery back in.
5. Plug charger cable back in. You should see it charging again.
6. If not, repeat steps 2-5. Otherwise, snap the back cover back on!