"I think children in situations like this deserve to have the maximum degree of privacy," Giuliani told ABC News' Jake Tapper in the summer. "And the best way to preserve that is -- except to point out that you love them and care about them and you're very, very proud of them -- just don't comment about it," Giuliani said.
Rosenstiel argues the media largely respects the privacy of children who shy away from the media spotlight.
"They are not going to scrutinize these people the way they would a candidate or someone who was acting in a more political role," he said.
He points to first daughter Barbara Bush, the twin sister of Jenna Bush, who has grabbed far fewer headlines than her sister, in part because Jenna went on a press tour to promote her book about AIDS.
But many of the candidates' children in this election have taken on political roles.
Sarah Huckabee is campaigning with her father this week, and is his national field director.
"I've got the best job in the world," she says on a YouTube video circulating on the Internet. "I get to travel with my dad and call it work."
Cate Edwards, who has scaled back her law studies to campaign for her father, former Sen. John Edwards, says it's easier the second time around.
"Four years ago, I had basically no public speaking skills," she told ABC News' Raelyn Johnson. "You just want to be yourself, and that was very hard for me."
Now she said she feels comfortable enough to speak alone at events, and is keeping a diary to remember everything that happens.
"This is an incredible experience and you just want to absorb, as much as you can."
ABC News Kate Snow, Eloise Harper, Jake Tapper, Raelyn Johnson, Kevin Chupka, Bret Hovell, Z. Byron Wolf and Matt Stuart contributed reporting.