More than 100,000 Irish Traveller tickets have been cancelled in the last month because of the issue.
The Department of Transport said there are currently just three tickets available for the entire season, and that only one ticket was valid.
The tickets were issued as part of the Irish Travelling scheme, which was announced by Taoiseach Enda Kenny in September 2016.
The scheme allows Travellers to apply for a single travel card for the duration of their stay in Ireland.
In April 2017, the department said it had identified a number of “significant issues” with the scheme.
The department said the problems included issues with applicants’ names, addresses, passport numbers and passport validity.
“There are significant issues relating to the identity and validity of Irish Travelled card holders,” it said in a statement.
“The number of Irish card holders has significantly increased and it is not possible to fully verify all of the information submitted by applicants, so there is a high likelihood that this number is under-representing the population of Irish nationals in the UK.”
It also said there was “no indication that the scheme has been successful in deterring potential visa fraud”.
In June 2017, a review of the programme found “significant failings” and “significant concerns” with its operation.
The review, commissioned by the Department of Health, was published on June 21.
In a statement issued after the review was published, Minister for Health Leo Varadkar said the Department had begun a review into the scheme and that it was currently working with stakeholders to resolve the issues.
He said there were “no immediate plans” to roll back the scheme, but that the Department was committed to working with Traveller groups to find a solution.
“Traveller groups are in discussions with the department and with the relevant authorities to address the issues identified,” he said.