The hearing to appoint a bankruptcy administrator to the club's 50 per cent shareholder UBIG was due to take place on Monday after being postponed on Friday.
However, the judge hearing the case has been seconded to another matter and the hearing has been pushed back a further 24 hours.
Hearts cannot complete a pence-in-the-pound Company Voluntary Arrangement with their creditors and exit administration until UBIG has appointed its own administrator.
But even if the case is heard on Tuesday, the name of the administrator could take another 30 days to be revealed by the court.
Hearts' administrator Bryan Jackson claimed on Friday, however, that the initial postponement ''changed nothing'' in relation to his attempts to save the club.
Jackson was given the go-ahead to start the CVA process last week by the administrator of Ukio Bankas, another firm once controlled by former club owner Vladimir Romanov which has also been declared insolvent.
Ukio Bankas, which owns 29.9 per cent of the club and holds a floating charge on the stadium, and UBIG are owed around £24million.
BDO, the firm handling Hearts' administration, has appointed fans' group the Foundation of Hearts but it must now wait for the UBIG situation to be resolved before it can finalise its deal.
A post of the FoH official Twitter site confirmed the postponement. It said: "UBIG court case now set for tomorrow, when the hope is the judge overseeing case will be available to preside."
Hearts lost 2-0 to Kilmarnock on Saturday to leave them 15 points behind St Mirren at the bottom of the Scottish Premiership.