NHS Lothian has been forking out £1.4 million a month to IHSL since February 2019 when the building at Little France was formally handed over.
The hospital was due to open in July 2019 but the transfer from the current site at Sciennes was halted at the last minute after final checks revealed the ventilation in critical care had not been built to the correct standard.
Some services have now moved into the new building, but the latest date given by Health Secretary Jeane Freeman for the hospital to be fully open is March 23.
NHS Lothian has confirmed payments to IHSL are to increase by an undisclosed amount to reflect the maintenance costs of the new ventilation system.
Edinburgh Western Lib Dem MSP Alex Cole-Hamilton said: “This really does add insult to injury. We have a state-of-the-art facility which is only being used to a fraction of its capacity 18 months after it was supposed to open and is already haemorrhaging £1.4m a month. To now learn these payments are going up is a hammer blow to staff, patients and families alike.
"The Scottish Government is pleading poverty over things like its refusal to build a new Eye Pavilion and yet we are shelling out untold sums to a private consortium.”
The new Sick Kids was built under the Non-Profit Distributing (NPD) system, the Scottish Government's version of controversial private financing models such as PFI.
Construction costs were £150m but the total cost over the next 25 years, including maintenance and facilities management fees, will be £432m.
NHS Lothian director of finance Susan Goldsmith said IHSL was responsible for maintaining the new ventilation system. "Therefore, allowances for maintenance and life cycle replacement are costed as annual amounts and are incorporated into the unitary charge.
"This is not unique to this project but is standard to all Public Private Partnership projects where changes are instructed to reflect, for example, new healthcare standards or clinical service changes. Such costs are obviously offset by any maintenance or lifecycle on equipment."
An IHSL spokesman said: "There will be an increase in the maintenance costs which will be reflected in the unitary payment."