Kokkinakis pulled out hours before his scheduled centre court clash on Wednesday night in his home city because of a shoulder injury.
The ailment casts doubt on the 29-year-old playing in the Australian Open starting Sunday in Melbourne.
"Very sad to have to pull out of my favourite event," Kokkinakis posted on Instagram.
"Unfortunately my arm isn't quite ready yet after missing a year off."
Kokkinakis played through pain on Monday night during a  courageous three-set win over American Sebastian Korda in the first round.
That match was the South Australian's first singles match in almost a year, following radical pectoral surgery in a bid to long-standing problems.
Kokkinakis's departure came as countryman Vukic continued his winning ways with a triumph against Italian qualifier Andrea Vavassori.
But a fellow Australian, Rinky Hijikata, was outlcassed by top seed Alejandro Davidovich Fokina with the Spaniard winning 6-3 6-2.
Vukic, who dumped two-time grand slam finalist Stefanos Tsitsipas from the tournament in the first round, prevailed 6-2 7-6 (7-5) over Vavassori.
Including qualifying, the match was Vukic's fourth in as many days in what he described as perfect lead-in to the Australian Open.
"It's the fourth day in a row but I was talking to my fitness coach and we just said it's a great way to prep for AO," world No.87 Vukic said.
"Challenge the body, get some physical matches, physical sets.
"Right now, with where my ranking is, every week is really important.
"I'm not top 30 in the world so I don't have the luxury of maybe taking it easier this weak or really focusing on the Aussie Open.
"For me, every week is important; every match is an opportunity to get better and improve my game."
Vukic set up a quarter-final against second-seeded American Tommy Paul, who defeated compatriot Reilly Opelka 6-4 6-4.
The Australian said he would adopt the same mentality as against Tsitsipas.
"It will be a great test to see again where I'm at early this year," Vukic said.
"I feel good, I feel like my game is progressing.
"There's things I can do better but it will be a different type of opponent and will be a great match to play."
The Adelaide tournament lost its third and fourth seeds in upset results on Wednesday.
Argentinian third seed Francisco Cerundolo was beaten by Spain's Jaume Munar, who won 3-6 7-5 6-4.
And Frenchman Ugo Humbert stunned fourth-seeded Dutchman Tallon Griekspoor 6-4 6-1.
Australian wildcard Rinky Hijikata meets top-seeded Spaniard Alejandro Davidovich Fokina on centre court on Wednesday night.
