The group signed a letter last year saying they felt that an increase in co-productions and 'bought in work', and a lack of self-produced shows had a negative impact on employment for Irish based artists.
Several meetings between the interested parties have taken place over the past year however the group say the situation continues to have a negative impact on the theatre 'ecosystem'.
In correspondence to the signatories, seen by RTÉ News, the Abbey Board said it was satisfied it had delivered on its commitments to the theatre sector and that it wanted to have productive communication and engagement with the entire theatre community.
It also said that 17 agreed actions which it committed to in 2019 have now been completed.
The board also said it was satisfied that the directors of the theatre are working to deliver it's five year strategy, which aims to nurture and reflect Ireland's artists in all their diversity.
However representatives of the signatories are to meet the Minister for Culture, Heritage and the Gaeltacht on 13 March and are planning a larger meeting later in the month after which they say they will be urging the Department and the Arts Council to resolve what they say are their continuing concerns.
The Arts Council has said it would commission an independent expert review of the Abbey's programme over recent years to help inform discussion on these issues.