Rooney oversaw his ninth league defeat on Saturday as Plymouth were thrashed 4-0 by Bristol City at Ashton Gate.
The loss to Bristol came just four days after a 6-1 beatdown by Norwich City.
Plymouth's back-to-back defeats now has them sitting 21st in the Championship on 17 points, two points clear of the relegation zone.
Rooney's side have also conceded the most goals in the league with 38, five more than Luton Town who boast the Championship's second-worst defence.
The Pilgrims' away form is of particular concern, having taken just two points all season.
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talkSPORT understands that the club want to give him time to turn it around.
Speaking to talkSPORT's Laurence Mora after the 'frustrating' Bristol City defeat, Rooney conceded he couldn't blame the travelling Plymouth supporters for their heated reception of the team.
"I think for the fans, we're grateful we see the support again," Rooney said.
"And it's very difficult to say to the players - you're almost embarrassed walking over to the fans and showing your appreciation."
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Rooney added: "If I was a fan I'd probably be a lot more angry than what they are. I think it's nowhere near good enough and we have to fix it quick.
"We need to find a way. I've tried going up to players, I've tried to encourage and support the players.
"I've tried everything really. I need to keep trying to find the right balance and the right way to make sure I get better performances, particularly away from home."
The Plymouth role represents the fourth stop in Rooney's managerial career.
He transitioned from player to coach while at Derby County and lasted 85 games in charge at Pride Park before he resigned ahead of the 2022/23 campaign.
Rooney was appointed as manager of Major League Soccer side D.C. United, where he spent two seasons as a player, just days after he left the Rams.
But the Manchester United legend was lured back to England when Birmingham City surprisingly axed John Eustace in October last year and replaced him with Rooney.
However, Rooney's tenure with the Blues proved to be ill-fated as he won just two of his 15 games in charge before he was sacked on January 2.
Birmingham ultimately could not recover from Rooney's troublesome spell as they were relegated to League One for the first time since 1995.
Rooney was given another chance as a Championship manager by Plymouth on May 25, but with the Pilgrims still yet to register an away win all season, time is evidently running out for the 39-year-old to turn things around.
Plymouth return to action on Saturday when they host 17th-placed Oxford United, who have lost three of their last four games.
The Pilgrims will then welcome Swansea City to Home Park three days later.