A site at the Ewart Library was picked as the preferred location by Dumfries and Galloway Council last year.
It later agreed to take forward plans for the most expensive of three potential options for the project - including a revamp of Loreburn Church.
However, a bid for lottery funding to support the project has not proved successful.
The scheme aims to create a new home for a vast collection of historic documents currently held by the council in various locations.
The council said the development of the centre could also contribute to local regeneration and cultural tourism.
The project was designed to safeguard the historic documents - some of which date back as far as 1452 - while also improving public access to the archives.
A £6.2m price tag was attached to the option for the development which was finally selected by the council.
Annual running costs were estimated at £250,000.
Plans for a £6.2m archive centre for Dumfries have failed to secure Heritage Lottery Fund support.