The secret to finding these disappearing emails is to use the all-encompassing search operator in:anwyhere.
Performing a Gmail search using this operator makes the search look everywhere. The significance of this is that a standard Gmail search does not look in your trash or spam folders, but an in:anywhere search does. In my experience, the majority of ‘lost’ emails are actually sitting in either spam or trash, having been accidentally marked as spam or accidently or purposely deleted.
Performing an in:anywhere search is simple, just add the operator before your search term.
Now you know the secret, happy email hunting!