One court official told Doha News that it would be the last time Al Kuwari could be tried "amicably" for the hearing.
After that, she loses the chance to mount a defence, the official said.
The triplets' father, Martin Weekes, said he was angry and disappointed that Al Kuwari failed to show the judicial system and families of the victims the common courtesy to show up.
"The delay in the legal system is beginning to shed an unfavourable light on the country and the courts."
The delay was prolonging the victims' families pain and grief, he said, and their patience was wearing thin.
"We call upon the Qatar Government to put an end to this insult and injustice.
"Once again, families and representatives from our governments attended court. We have continued to show more respect to the judicial system than some of the defendants."