You can add more hydrogen peroxide to keep the reaction going longer. This will be necessary if you have a lot of material (more than the size of a penny). You should use a solution of 35% hydrogen peroxide or stronger.
For example, if you add 30 mL of hydrogen peroxide, you will need 60 mL of vinegar.
Note that this reaction takes a long time, and it is not particularly effective. If you have a large object or a thick layer of copper, another method should be used. Just to remove the copper from a penny it could take hours or days. Remove the object when you are finished and pour the solution into a labeled bottle. The solution should be turned over to a professional waste contractor.
Plastics and many metals will be dissolved using this method. Only place items that are made from gold, platinum, iron, nickel, aluminum, chromium, or cobalt in the beaker.
Nitric acid is a strong acid. Wear gloves and goggles. Do not get the acid on your skin or in your eyes. Do not inhale fumes from the acid, and do not ingest it. Nitrogen dioxide is toxic. This must be done in a fume hood or other well ventilated area. Do not inhale the nitrogen dioxide. If you do get the acid on your skin or eyes, wash with water for 15 minutes.
You should use tongs to remove the material. Do not put your hand in the solution! The reaction is complete when no more gas is being formed.
You should also consider the material underneath the copper. If you are dealing with a soft metal or plastic, a grinding wheel might do more damage than a sander or sand blaster.
Inhaling metal shavings can be dangerous. Metal shavings can cut your eyes if they get in them.
For example, you might use a 180 grit sandpaper to get out the initial scratches, and the move to a 300 grit sandpaper to smooth things out even more (a higher grit produces finer scratches).