Cases are so delayed victims are, in some cases, unwilling to pursue them. There are also concerns delays mean sheriffs are less able to impose special bail conditions and victims are being put at risk.
The specialist court was lauded for its pioneering approach of giving victims multi-agency support, and it was launched amid expectations perpetrators would be dealt with within six weeks.
However, it is now seeing cases delayed by up to 40 weeks, and the sheer volume of cases means rather than one specialist sheriff covering the court, a number of sheriffs are sitting.
In a dramatic shift from their traditional zero-tolerance approach to domestic abuse where alleged perpetrators are taken into custody, police and prosecutors are looking at whether perpetrators could be released on special police-imposed bail conditions to avoid clogging up the courts.
Mhairi McGowan, head of service at Assist, the expert advocacy and support service for victims of domestic abuse, said: "The delays in the domestic abuse court are having an impact, not just on the quality of evidence, but on whether there is evidence able to be heard at all.
"Victims are routinely waiting for five months for a case to be heard and for some victims, it can be as long as a year. I can only imagine how difficult that is.
"On a positive note however, agencies have changed how they deal with domestic abuse and victims are coming forward to report their experiences. They rightly expect and deserve a robust response. The court was set up to ensure victims would receive a better deal, and also perpetrators would be brought to justice.
"Surely a solution can be found to end these delays? However, it must be based on reducing the risk to the victim and not on a quick fix that leaves the underlying problem unresolved."
The Glasgow court was first set up as a pilot by the Labour-Liberal Democrat administration in 2004.
A specialist domestic abuse court was set up in Edinburgh last year on a similar model with specialist prosecutors, police liaison officers, advocacy workers and sheriffs working together.
Chief Superintendent Bob Hamilton of Police Scotland said: "This is as a result of our successes. We are locking up more people than ever before. The cases are more complex. The length and nature of the investigations means they are really complicated as we are looking at so many historic cases, and that is having an effect on the court.
"In Glasgow they have added another court but cases are taking longer. It will need work to ensure we are not blocking up the system and that we are still identifying the top-end offenders."
Focused police drives to tackle domestic abuse and increasing confidence among victims have seen recorded incidents rise dramatically from 35,877 in 2002 to more than 60,000 last year.
He added: "We are currently working with the Crown on releasing people on special bail conditions rather than just custody, but we have got a lot more work to do to ensure we have mitigated the risk of reoffending. That should help to ease the burden on the court.
"If we are going to release people on an undertaking, we need to ensure safeguards are in place."
A spokesman for the Crown Office said: "COPFS looks to deal with domestic abuse cases as a priority, and we work closely with the Scottish Court Service (SCS) to schedule the cases as quickly as possible. Public safety is paramount. The use of undertakings in domestic abuse cases would only ever be introduced after a full evaluation and risk assessment had been carried out with the Police and support agencies.
"COPFS takes domestic abuse extremely seriously. There is no place for it and no excuse for it.
"Our prosecution policy is clear and robust: all cases of domestic abuse involving violence or threats of violence, where there is sufficient available evidence, will be prosecuted.