Acton, 25, was charged with "other contrary behaviour" after an incident in their defeat by Catalans on 1 July.
The case was adjourned on 4 July for one week after Leigh requested more time to prepare for the hearing.
He is accused of grabbing Greg Bird's shirt, lifting him and then pushing him to the floor as he lay injured.
The secondary delay request was granted, provided Acton does not play for Leigh in Friday's match against Huddersfield.
Acton has already missed a 50-10 defeat by Warrington after the case was adjourned the first time.
He was charged with a Grade F offence, the most serious on the Rugby Football League's disciplinary scale, which carries a minimum ban of eight games if found guilty.
Meanwhile, Warrington forward Ben Westwood has been given a three-match ban for a Grade D dangerous throw offence in their win over Leigh, and Salford centre Junior Sa'u will serve a one-match suspension after submitting an early guilty plea over a Grade B high tackle charge.
Leigh Centurions forward Jamie Acton's disciplinary case has been delayed for a second time so his legal representative can attend.