Poggio Colla is one of the few sites offering insight of the Etruscan life in a non-funerary context. It spans most of Etruscan history, being occupied from the seventh to the second century B.C.
Centering on the acropolis, a roughly rectangular plateau, the site was also home to a sanctuary: numerous votive deposits indicate that for some part of its history, it was a sacred spot to a divinity or divinities.
The abundance of weaving tools and a stunning deposit of gold jewelry discovered in previous excavations, have suggested that the patron divinity may have been female.
In this view, the ancient depiction of childbirth becomes even more interesting, according to Greg Warden, professor and associate dean for academic affairs at the Meadows School of the Arts at SMU and a director of the Mugello Valley Archaeological Project.
"Might it have some connection to the cult, to the kind of worship that went on at the hilltop sanctuary?," Warden wondered.
Perkins speculated that the woman giving birth could be a representation of an Etruscan goddess, suggesting that Poggio Colla was the location of a cult-site for an Etruscan fertility goddess.
"She would represent a new Etruscan myth, as we know of no Etruscan goddess who gives birth in Etruscan mythology," Perkins said.
A few observations:
Of course they haven't found representations of women giving birth at burial sites. Those sites were set up as houses for the dead supplied with things as if they were still living. Very pyramid-like.
This doesn't necessarily imply an unknown Goddess. The shard could be from a votive piece, buried at the site of the temple asking for a healthy birth.
We know little of Etruscan lore, but what is out there labels Uni the Mother Goddess and the one to petition for Fertility. She is syncretized with Juno, aka Iuno. Iuno... Uni... Hmmm... Also, like Iuno/Hera, Uni is related to the hero the Romans call Heracles and alleged to be his Mother, not his step-mother. There is art depicting the relationship too. So yeah, we might know of an Etruscan Goddess who gives birth ;)
Here's an interesting article on Uni, tho nothing is cited.
A link within the article above leads to a story from 2010 about the discovery of an Etruscan home, not a burial site. Also, religious sites have been discovered, including temples. Looks like the Etruscans are revealing their whereabouts as well!