It's hard to blame kids for acting like their parents have taught them to act (i.e. keep whining until you get what you want). After all, behavior which gets rewarded, gets repeated.
But there is a point where being persistent becomes rude, even if you're a kid...and kids are well aware of that. When our DD7 crosses that line, one of us just asks her, "What part of 'NO' don't you understand?" Kids do understand 'no,' they just try to pretend it doesn't exist when it serves their purpose.
I think the "I'm sure you understand" strategy is the best approach, and as others have said, you have to be firm with it. Not, "well maybe," or "we'll see."
More like, "No. Not this time -- this is going to be just us."
And let that be the end of the discussion -- or as DW sometimes tells DD7, "Asked and answered. Next?"