The teenager, from Castlederg in County Tyrone, was last seen being driven away by convicted child killer Robert Howard in August 1994.
She had been on a night out in Donegal. Arlene's body has never been found.
Howard, who died in prison last year, was acquitted of the 15-year-old's murder in 2005.
At the latest preliminary hearing at Belfast's Coroner's Court on Thursday, a barrister said the family  is "becoming more and more upset" at the delays.
He said authorities in Dublin are yet to hand over documentation about Garda investigations into the schoolgirl's disappearance.
The court was told representatives for the coroner met officials from the Chief State Solicitor's Office and An Garda SÃ­ochÃ¡na (Irish police) in Dublin to discuss the case in September.
There has also been further communication via email, letters and telephone, the court heard.
The coroner said he shared the family's frustrations but was "reassured that the state solicitor's office is taking this matter forward with consciousness".
He said it was important that "we do not let this matter slip".
The most recent searches for the teenager's remains on farmland in County Tyrone last month were unsuccessful.
Howard was acquitted of the teenager's murder by a jury not told about his conviction for killing another teenager in England.
A further preliminary hearing has been scheduled for later this month.
The family of Arlene Arkinson is "deeply frustrated" at delays in concluding an inquest into her death, a coroner's court has heard.