Supposedly the ancient Romans believed that one's body and soul renewed itself every seven years, which is probably the origin of this myth.
Regrettably, I can't find a good citation on that, although it's widely cited as the origin for the superstition that breaking a mirror causes seven years of bad luck.
As a complete aside, I can explain the 7 years of bad luck.
Back in the 1500's and up, when mirrors were smoothed silver on glass, they were only for royalty. And as per royalty, there were servants. The "bad luck" was actually punishment of 7 years of indentured servitude to pay for a broken mirror.
Regrettably, I can't find a good citation on that, although it's widely cited as the origin for the superstition that breaking a mirror causes seven years of bad luck.