Advocates hoped there would be an outcome on Thursday after three days of Senate debate, including late into Tuesday and Wednesday nights.
Bec Paterson, 24, who was diagnosed with mito as a teenager, carries the genetic change which can cause the disease.
Ms Paterson said while it was frustrating to see how slowly the legislation was moving, she remained hopeful an outcome on Thursday would provide a reason to be positive about the future.
"Every day it's delayed in the Senate means one step further away from my partner and I from having children," she said.
"Time is running out. But, if Maeve's Law is passed, it will provide hope and encouragement to so many, that things can finally move forward."
The bill is commonly referred to as Maeve's Law after five-year-old Maeve Hood who has a severe type of mitochondrial disease which was diagnosed at 18 months.
Her Leigh syndrome diagnosis means Maeve might not live past her next birthday.
More than 50 children are born with mitochondrial diseases each year.
The treatment involves replacing mitochondrial DNA from the mother with healthy mitochondrial DNA from the egg of a donor, allowing them to have a biological child who would not inherit a predisposition to the disease.
Labor senator Murry Watt told the chamber about baby Chloe Mets who was conceived by IVF before experiencing "unpredictable and traumatic" mito episodes.
Chloe was in and out of hospital for about six weeks before she died.
Bethany Hodge grew up watching her sister suffer from tremors in her hands, hearing loss, speech impairment and intellectual delay.
"I consider that this bill is an important step in ensuring that families like Joanne's and Bethany's can live without the devastating pain that this disease causes," Senator Watt said.
Greens senator Jordan Steele-John said the legislation gave parents the choice not to pass this genetic abnormality on to their child.
"Fifty-six kids will lose their lives to mitochondrial disease every single year. Let it compel us to act to ensure that this suffering is not visited upon others," he said.
Centre Alliance senator Stirling Griff said he would support the bill to help Australians touched by mitochondrial disease who " want to see a relatively small change in law but one with massive ramifications".
But some senators, including Labor senator Kristina Keneally, Liberal senator Matt O'Sullivan and One Nation senator Malcolm Roberts, expressed reservations about the bill on ethical and scientific grounds.
Labor has been granted a rare conscience vote on the issue.
Senator Keneally said just because members voted against the bill didn't mean they were against scientific progress, speaking of her stillborn child who died of a genetic condition.
"Yet I can't support this bill because in my mind, based on both ethical convictions and the paucity of the scientific evidence, I have serious concerns," she said.
"Just because we can doesn't mean we should. This is an incredibly intrusive power (and) intervention in human existence."
Nationals senator Matt Canavan said he couldn't support the bill because it involved the destruction of life and the removal of the prohibition on transferring genetic material between two human beings.
Senator Canavan moved amendments disallow a fertilised egg being destroyed and to remove immunity from civil actions relating to mitochondrial donation licences.
Amendments by senator Canavan on the two issues are still before the chamber but others he presented were voted down.
The Greens failed to force a vote on Thursday, with the Senate not readjourning until the end of March - the last time before the election - when it will also have to deal with the federal budget.
Finance Minister Simon Birmingham said he would work to ensure enough time was allocated in the next sitting week to vote on the issue.
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