Latest weekly figures show the hospital has only met the target of 95 per cent of emergency patients being seen within four hours on two occasions between the beginning of November and the end of March.
And one week in December performance dipped as low as 88 per cent of patients seen within the target time.
It is the worst figure for the hospital since the four-hour target was introduced in 2007.
NHS Lothian said a combination of factors, including a lack of space and an increase in night-time cases, was to blame. They also had to deal with more cases due to the temporary closure of the children’s ward at St John’s Hospital, Livingston.
Previously, the Sick Kids comfortably met the 95 per cent target most of the time, only occasionally falling to 94 per cent.
Lothian MSP and Tory health spokesman Miles Briggs said: “It will be really concerning to Lothian parents and families that emergency waiting times worsened significantly towards the end of last year and have often been below target since.
“Staff at the Sick Kids do an incredible job for the city’s children but these statistics suggest they are under real pressure.”
In a letter to Mr Briggs, NHS Lothian chief executive Tim Davison said there had been an increase in emergency medical admissions during the winter.
But he said other factors were a lack of physical space in the emergency department, which affected efficient patient management; an increase in evening and overnight attendances when staffing levels were lower; a rise in West Lothian cases during the St John’s closure; and longer turnaround times in getting blood results back because laboratory services were off-site in the evenings ahead of the move.
He said: “The move to the new hospital will provide the service with a properly sized and configured emergency department and we are investing in more staff specifically to address the rise in night time activity.
“Laboratory services will be on the same site, which will speed up turnaround times and decision making. The new hospital also has an expanded Acute Medical Receiving unit with more beds, which will support the rise in emergency admissions.
“The service are rightly proud that their four-hour performance is usually very good and they look forward to the benefits they will see in the new hospital where they will be working hard to ensure they meet and maintain the 95 per cent target.”