An earlier 06.15 GMT Belfast departure time had been due to begin at the end of January.
But the journey time would have taken longer - almost two and a half hours.
However Translink has now said that "alternative options" are being looked at. Passengers have been consulted by Translink and Iarnród Éireann about the proposed changes.
The service is operated jointly by Translink and Iarnród Éireann.
"The companies will work together to review feedback from the timetable consultation processes," a statement from Translink read.
It added they hoped to finalise a new timetable by the end of "the first quarter of 2016".
Translink has postponed the introduction of a new timetable for the Enterprise train service to Dublin.