One of the principal arguments I've come across from No campaigners is, in absence of any objection to the Treaty itself, that having a second referendum is undemocratic, and that the people who voted No last time should be respected. The difficulty with this argument is that respecting and listening to the No voters is exactly what has led us to have this second referendum.
After the last referendum, it was quite clear that a renegotiation of certain aspects of the treaty was on the cards. The two biggest No campaign groups, Sinn Fein and Libertas, had both campaigned on the basis of going back to the EU and renegotiating on their contentious issues. Furthermore, no less than 76% of No voters believed that the No vote would be used to "renegotiate exceptions within the treaty", which gave the Government a clear mandate to seek this new deal before putting the treaty back to the people.
Which is exactly what the Government did. The biggest issues for No voters in the referendum were 'Loss of Commissioner' (which 71% of No voters said was somewhat/very important to their vote), 'Neutrality' (82%), 'Workers Rights' (82%), 'Abortion' (66%) and 'Corporation Tax' (72%), which were unsurprisingly the points which the main No groups campaigned on in the run-up to the referendum. These top issues are the very ones which the Government received guarantees on from the 26 other member states, guarantees which state in the most unequivocal terms that these matters will be decided at national, not EU, level.
While I can certainly accept that a No voter might not be happy with these guarantees, might feel that they don't address his or her specific concerns, it would be disingenuous to suggest that the Government doesn't have the right, after listening to the voters and attempting to address their worries, to put this new deal back to the people for a second vote, and allow the people a chance to say whether their concerns have been met or not.