How do capacitors maintain their charge?
While the battery is present:
The copper wire connected to the positive end of the capacitor will also be saturated with positive charges (absence of electrons).  The copper wire attached to the negative end of the capacitor will also be saturated with negative charges (presence of extra electrons).

When you remove the battery:
When the battery is removed, you don't have an uneven charge distribution along the plate&amp;copper (the plate and the copper lead will both be charged) and the charges will not be moving anywhere. The charges will stay in place.