"They're very loving, very close children. I can still talk to my older son and have long, lengthy conversations cuddled up on the couch with him. He will on his own accord, if we're watching a movie, come and sit down next to me and rest his head on my shoulder, put his arm over my shoulder, come talk to me about whatever's bothering him at school," she said.
"I really feel that there is an extra bonding or attachment there that I would like to think that because he nursed until he was 6, that there was some more closeness there ... that you get when you're able to have him in your arms for a longer period of time," she said. "My daughter's the same way. Very much so."
When Siobhan sees Tiernan with their mother, she said, she wishes she could still do it sometimes.
"But I'm getting older and I'm just happy to see them doing it," she said.
But it's not just Paul's older children who say it is all right that Tiernan still breast-feeds. Her husband said it's no problem, too.
Paul said she is able to distinguish between being her children's comfort object and being a sexual partner for her husband.
"I compartmentalize it," she said. "When I'm with my children and they need to nurse, then I'm mom. When I'm in the bedroom with my husband, I'm his wife and we have our intimate time. It's very much, they're two totally separate things."
Though their children seem happy now, some may ask late breast-feeding moms whether they're doing what nature intended or taking a good thing too far. With no long-term studies, the jury's still out.
"Who wouldn't want to stay with mother's love, mother's nourishment, for their entire life?" Braun said. "It's a very seductive pull. But I think a mother's main job is to work herself out of a job."
Despite getting some negative feedback from people who disapprove of her choice to continue breast-feeding, Paul said she is not going to stop. She said she believes she is giving her son the best start she can in life.
"I'm comforting him, and when he's ready he'll quit," she said.
Paul said she hopes that more women will choose to breast-feed their children past infancy.
"This is a wonderful way to parent and nurture our children and give them the start that they deserve in life," she said. "You know, in other places in the world this is perfectly normal. There's nothing wrong with this and there isn't anything wrong with it. We just aren't used to seeing it in this country."