Up to 100 families could be affected by a delay in providing paediatric surgery.
The problems have occurred at Craigavon Area Hospital and Daisy Hill in Newry.
Although the Southern Health Trust did not give a figure for the number of operations delayed, the BBC reported that it involves as many as 100 families.
The Trust has apologised for the "regrettable delay".
A trust spokeswoman said: "We are very sorry for any distress or inconvenience that has been caused."
Some parents claimed they have not been kept informed, despite lengthy delays in their children's treatment.
Philippa Dougan-Toal, whose five-year-old daughter Amelia is due to have surgery, is among those affected.
"We were told from the day we went to our GP that her case was urgent. Obviously, as a parent, you hear mention of a biopsy and that's all you can think of," Philippa told the BBC.
"We were told we'd hear straight after Easter, by late April we'd still heard nothing.
"We rang and all the person we spoke to could tell us was that paediatric operations weren't being done.
"That was it. There was no explanation and no indication of when the operation would be done."
Newry and Armagh Sinn Fein MP Mickey Brady is due to meet the Southern Health Trust today. He said the delay was unacceptable.
Mr Brady said: "Children's theatres in both Craigavon and Daisy Hills hospitals have not been running at full capacity.
"This is a completely unacceptable situation which needs to be rectified as a matter of urgency."
The trust spokeswoman said both Craigavon and Daisy Hill hospitals have adopted new ways of working which have meant changes in the way services are provided.
"Although children's emergency surgery has continued as normal, our children's theatres have not yet been running at full capacity," she said.
She said children's surgery would be fully operational again by the start of June and that patients would be contacted about surgery dates.