How many rounds does it take to edit a manuscript?

It takes as many rounds as it takes.

I am on the third and final round of revisions with Whisper Falls, and the manuscript is getting ever closer to perfection. 

Round one focused on big picture changes. Normally, that would involve rewriting shaky parts of the plot.  Mine didn't change much, although I did simplify a subplot for a minor character.

Round two took a deeper look at the characters, their choices, and their reasons for those choices. I didn't change the personalities or voice of any characters—not the hero, heroine, or secondary characters. However, I did add lots of backstory (at least, that is what I call the stuff I added. My editors call the new details essential to understand choices and motivation.)

Round three revolves around refinements. Does the story flow organically from start to finish? Are there any continuity errors? Will readers from all around the globe be able to visualize the North Carolina setting from my narrative?

This last question has been the hardest to resolve. I've lived in North Carolina for so long that I've forgotten how unique this location might be.  Consequently, I've had to sprinkle in several details to enhance the ability of readers to visualize my beautiful home state. My editors, who live in New England, have proven invaluable for these revisions. Weather, flora/fauna, topology, lifestyle—even school calendars—can differ dramatically.  For instance, my hero likes to bike through a park near his home.  The park in question, Umstead State Park, is 5000 acres.  That is NYC's Central Park times seven.  Apparently, parks aren't that big in New England, hence the need for a deeper description.

I should have my final revisions completed later this week.  And then, Whisper Falls will be really and truly done. A few copy-edits later, we go to print!