On Tuesday, the volatile attacker found himself in the spotlight again after his glaring late miss cost Austria the chance to draw with Germany and avoid their eighth successive defeat against their neighbours.
"I want to apologise to the whole country," said Arnautovic, who contrived to scuff the ball wide from point-blank range with the goal at his mercy.
"It was my mistake. It was a perfect ball to me, so there is no excuse. We were clearly superior and... the Germans won with luck," he added after the 2-1 loss in the World Cup qualifier.
Until then, it had been an encouraging performance from the 23-year-old, who provided the pass for Zlatko Junuzovic's goal and continually troubled Germany down the right flank.
Variously likened to Cristiano Ronaldo and Zlatan Ibrahimovic, Arnautovic was once described by former Austria international Andrea Herzog as the best player the country had produced in the last 30 years.
But so far, Austrians have seen only exasperating flashes of his talent.
As a teenager, he was widely criticised after being sent off in an under-19 tournament, was regarded as too individualistic and had trials at three Austrian clubs before being signed up by Dutch first division club Twente.
He joined Internazionale in 2009 but coach Jose Mourinho took an instant dislike to what was seen as a lax approach and he made only three appearances in their treble-winning season. In the meantime, he was also dropped by Austria.
After one season, he moved to Werder Bremen, saying that he was more disciplined and set three alarm clocks to make sure he got to training in time.
It did not last long and appearances were again limited by disciplinary problems.
He managed only three Bundesliga goals in his first season, fell out with his team-mates, was banned for three games after being sent off and again found himself sidelined by his country, having earned a short-lived recall.
The low point came when he was dropped by Werder's exasperated coach Thomas Schaaf following an incident at a nightclub, which Arnautovic said had begun with an unprovoked attack on his brother.
Last season saw slight improvements up until March, with Arnautovic scoring six goals, when he tore a knee ligament while playing with his dog, an incident described as "frustrating" by Schaaf.
This season began, as usual, with promises to turn over a new leaf, insisting that the birth of his daughter had made him more mature and responsible.
"I must keep myself under control," he said before the Germany match. "I have a big responsibility as a father and that helps me to become more sensible."
"It's better that I keep my mouth shut and let my feet do the talking.
Austria, where football has to compete with alpine skiing for attention and which has struggled to produce players in the last few years, can certainly not afford to see his talent go down the drain.