"Plaintiffs were also told by defendants that the other cryotanks could not be searched to determine whether or not their straws were there, without jeopardizing the integrity of other patients' embryos, and that no further search would be conducted," according to the lawsuit.
The couple insists that the most logical explanation is that the embryos were mislabeled and later implanted in another woman.
The lawsuit alleges the embryos have been unaccounted for since 2008, when they were harvested and frozen.
"They can't find them," he said of the straws. "There is no record of them being destroyed or at the bottom of the tank. Originally, they contended they were unable to examine the tank, which is routinely done by all clinics."
In vitro fertilization -- the most common kind of assisted reproductive technology -- was pioneered in 1978 by doctors in the United Kingdom, and has been used in the United States since 1981.
Of about 62 million women of reproductive age in 2002, about 1.2 million, or 2 percent, had an infertility-related medical appointment within the previous year, and 10 percent had an infertility-related medical visit at some point in their past, according to the Centers for Disease Control.
In 2008, 361 U.S. clinics reported data to the Society for Assisted Reproductive Technology on 140,795 treatment cycles leading to the birth of 56,790 babies.
One of the most dramatic mishaps was in 2009, when the frozen embryos of Shannon and Paul Morell were mistakenly implanted in the womb of Carolyn Savage of Sylvania, Ohio.
Savage describes in her book, "Inconceivable," how she carried the baby to term and, with her husband Sean, gave the newborn boy back to his biological parents.
The Morells of Sterling, Mich., had survived the pain of miscarriages, two failed fertility treatments and even a diagnosis of profound deafness in their newborn daughter.
On Feb. 17, 2009, they received stunning news from the fertility clinic: All of their frozen embryos had been accidentally transferred into the womb of another woman -- and she was pregnant.
For 36 weeks, Savage carried the Morell's child, delivering a healthy 5-pound, 3-ounce boy, Logan.
"It was the worst thing my husband and I had to deal with," Shannon Morell told ABCNews.com last year. "We felt helpless."
"Nothing could prepare me for the empty feeling I experienced," wrote Morell in her 2010 memoir, "Misconception." "Worst of all, I could find no books to read for comfort, no similar stories to read for advice and practical tips. Our situation was unique; we were reluctant pioneers in the field of embryonic mishaps."
Both the Morells and the Savages have been critical of lax regulation in the fertility industry.
Walterspiel and Waters, who were unavailable for an interview for "privacy reasons," said they faced a similar tragedy.
"This is devastating for them to know that because they are several years older, their ability to create viable embryos is compromised," Vorzimer said. "It's even more disconcerting to them to have three babies out there or women pregnant believing it's their genetic child and it belongs to my clients."
The couple say they suffered "severe emotional stress and depression," knowing they might not ever have another biological child, according to the lawsuit.
The lawsuit alleges that care at Santa Monica Fertility "fell below the standard of care required of medical personnel in the community, and manifested a lack of that degree of knowledge and skill necessary" to take custody of their unused embryos.
"These things happen, but they are very rare," Vorzimer said. "The Octomom's doctor comingled embryos and in India there is a couple who ended up having twins that were not genetically related to each other."
"This is pretty horrific, considering the reputation of Dr. Jain and how prominent he was," Vorzimer said. "He had no shortage of patients at his facility."