Omitting "that" in a complex sentence is definitely a writer's prerogative but certain caveats must be observed to keep the sense of the sentence intact. I posted in the Forum on July 3, 2010 a two-part essay on "When to keep or knock off 'that'." Check out that essay by clicking this link to
"Getting a better handle on when to use or to just knock off 'that'.”For a systems appreciation of the grammar and semantics involved in the dropping or retaining of "that," I suggest a rigorous reading of my three-part essay on
"Getting to know the relative clauses better" that I posted in the Forum last November 17, 2013.
When you're done with these readings, I'm very sure that you'd have developed a sure knack for deciding when to retain or drop "that" from a complex sentence.
