The flagship tribunals were set up in Glasgow, Edinburgh and Ayr to fast-track cases in eight weeks while providing multi-agency support to those affected.
New figures reveal that cases are taking more than twice as long as expected. The waiting time for a domestic abuse case in Glasgow from its first calling to full trial was now 19 weeks, nearly four and a half months, according to the Scottish Courts Service [SCS] .
Mhairi McGowan, of advocacy group Assist, which is heavily involved in the courts project, pinned the blame for such delays firmly on the courts.
She said: "I believe that Police Scotland and the Crown Office are dealing with domestic abuse in an appropriate and robust basis.
"My issue is that the court system does not have the capacity to ensure that these cases are dealt with promptly. The target was eight weeks. The fact that cases are twice as long to come to trial makes a difficult situation much worse for everybody, victims, children and perpetrators."
Lily Greenan, of Scottish Women's Aid, said: "We don't have sufficient court resource. The court system is so clogged that people are being left in stasis. Domestic abuse courts were supposed to fast-track cases. Police have improved their systems immeasurably. Prosecutors are working on these cases full-tilt but this is being done in isolation from the court system."
Specialist domestic abuse courts now account for a quarter of summary cases that go through Glasgow Sheriff Court. First set up in 2004, the city domestic abuse pilot was praised in a Scottish Government report in 2007 and followed by an Edinburgh pilot in 2012, and a new "cluster" to handle such cases in Ayr.
Victims' advocates stress that their work is made much harder if cases drag out.
Ms Greenan said: "It leaves a lot more time for perpetrators to approach victims - even if they have special bail conditions - through wider family networks." There are also safety concerns over women - and most victims are women - who have to spend months waiting for an outcome of their case. There are concerns that victims may lose touch with vital advocacy groups, such as Ms McGowan's Assist, when cases are delayed.
Graeme Pearson MSP, Labour's justice spokesman, said: "It's really just not good enough for these cases to progress at a snail's pace, not for the victim and not for the perpetrator."
Figures for January 2014, obtained but not published by the party, showed waiting times of 22 weeks in Glasgow and 11 in Edinburgh.
In addition, there have been court delays caused by police officers being on Commonwealth Games duties who were unable to give evidence. The earlier figures also came before the courts service took action to speed up court business.
An SCS spokesman said: "While the long-term trend in crime is down, there have been significant increases in domestic abuse and sexual offence cases which reflect more proactive approaches by police and prosecutors and increased confidence amongst victims in reporting these crimes."
The service had responded by introducing additional measures to reduce waiting times. He added that it is working with colleagues on "medium and longer-term measures" to ensure an efficient flow through the courts.
The spokesman continued: "The latest figure for Glasgow is that the time taken between cases calling and trial is currently 19 weeks, down from 22 weeks in January 2014. For an adjourned trial the figure is 10 weeks. An additional trial court has already been added each Friday to the existing court programme and during October there will be an additional daily trial court to tackle business volumes."
Under the single force, the number of domestic violence incidents leapt from 39 per cent to 54 per cent of total crimes, meaning hundreds of extra cases.