The latest issue is linked to a mobile phone tower in Dapto in New South Wales, which affected 4500 users in the area on Sunday between 3am and 12:20pm.
A review by the Telco has included nine failed calls to triple zero, but Optus says those affected "are OK" and the issue has been rectified.
One of those callers required an ambulance and used another phone to contact emergency services.
Another was trying to call emergency services but couldn't get through and had made accidental calls.
The incidents have alarmed both Australians and the government, including Communications Minister Anika Wells.
Ms Wells has requested discussions with representatives from parent company Singtel, who she says will be visiting Australia this week.
The failure is the third time in two weeks a major Optus outage has prevented people accessing emergency services.
A scheduled firewall upgrade in South Australia triggered a communications outage on September 18 linked to the deaths of three Australians.
Optus chief executive Stephen Rue blamed human error for that fault.
Normal calls were largely unaffected, but the outage blocked about 600 triple-0 calls from connecting to emergency services.
It affected customers in South Australia, Western Australia, the Northern Territory and NSW.
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