Caroline Graham was living in Hanover Street in the Co Armagh town when she went missing in April 1989.
The 19-year-old, originally from Newry, Co Down, was living with her boyfriend at the time.
She had been at the Coach nightclub with a friend the night before she vanished.
She had stayed part of the night with her friend in a hostel in Portadown.
Over the past two years, police have stepped up their investigation and conducted searches and arrests.
Detectives have carried out a major search operation in the Carleton Street area of the town and have searched areas of waste ground and buildings, including a well.
Despite their efforts, however, the body of the teen has never been found and police believe she was murdered and buried somewhere in the town.
A 76-year-old woman was arrested on Tuesday in connection with the investigation and was later released unconditionally.
All I want is closure. We haven't even had the chance to hold a funeral because Caroline's body has not been recovered.
On Thursday, Caroline's mother Barbara urged those who knew anything about the murder to come forward.
She said: "It's been a sheer living hell for me not knowing where she is and what has happened to her.
"It is very hard to live with - everyone finds it very difficult. I have children and grandchildren and I have to keep going for them.
"I have 10 grandchildren and Caroline never got to know them and that is not right."
Mrs Graham appealed for anyone with information to contact police investigating the murder.
She said: "Just open up your conscious and give the police the information they need.
"I wouldn't like to see them walk in my shoes. If there is any good in them they will do what's needed.
"The police tell me the investigation is continuing but I would just like to appeal to anyone who knows anything to tell us. Please give us peace and lay Caroline to rest."
We believe Caroline was murdered and that her remains are somewhere in Portadown.
Detective Inspector Peter Montgomery
Detective Inspector Peter Montgomery said police were keen to speak with two soldiers, possibly UDR men from Omagh, who had given Caroline a lift in a black XR3i car before she went missing.
He said: "These men are not suspects, we just want to find out what Caroline may have been talking about before she went missing.
He went on: "We are grateful to those members of the community who have given us information.
"All our enquiries lead us to believe there is more than one person who knows exactly where Caroline is buried.
"We need them to come forward and tell us exactly what they know.
"Whoever is responsible for Caroline's murder may have spoken to people and they may know exactly what has happened to Caroline.
"I need to speak to anyone who saw Caroline at the Coach with her friend that night. Did you pick up Caroline and her friend and drop them off in Portadown?
"I also want to hear from anyone who has any information about Caroline's murder and where her remains might be buried. Has anyone talked to you about her murder or where she is buried?
"I want to say that if you have concerns about giving evidence, please speak to me to explore what might be possible in terms of doing so. We will do everything possible to allay any concerns you might have but the most important thing is for people to come forward - for Caroline, for her family and for justice."
Police can be contacted on 028 90700 727 or 075 8522 8283.