Spells which are already in play cannot be dispelled by Natural Dispels or Dispels from magic items. Such Dispels only work upon a spell as it is cast and not once a spell is in play.
There are a few specific exceptions to this, where spells in play are automatically dispelled if they come within a specified distance of certain magic items. However, generally speaking, spells which are already in play can only be dispelled by means of a Dispel card - not Dispels from magic items or Natural Dispels, and not other forms of counter magic. A Drain Magic card played against another spell will, of course, dispel all spells which are in play at the time.