If you are purchasing a wine stopper with a "cork" .
Cork stoppers are meant to keep air out of the bottle
during the evening as you consume the wine, not to seal the bottle for storage.

Place the cork in the bottle with a small amount of pressure, the cork will keep all the air from reaching the wine.

To remove the cork twist the cork out of the bottle, never rock the cork from side to side.

The above is also true for glass stoppers and steel cone stoppers with the rubber rings. None of the stoppers above are meant to be used to seal a bottle for storage, and they should not be forced deeply into the bottle.

We have wine stoppers that seal for storage and can be used even if you store the wine bottle on its side. This is the stopper to buy if you want to store your wine for another day.  A problem I never seem to have.
 

You can find storge stoppers at:  www.winestoppershop.com/KeepFreshStoppers.html