If the subject-matter or circumstances of the "repeat" referendum are sufficiently different, there is no difference from elections.
Yeah, I know the typical argument against referendum repeats is the "democratic deficit" they supposedly have by asking the "same question". (I'll come back to this.) But before we get to that: one could ask the question in reverse: why would a candidate that has failed an election be allowed to run again later for the same office?! After all, the public said no to him. Should he be allowed to run until he gets his way? Of course, even if all candidates are exactly the same on a later ballot, chances are something has changed: their platforms etc.
Now as for the "same question" referendums, the much criticized repeat referendums for EU Treaty changes/adoptions didn't ever have the exact same question, even if it was nominally the same on paper. There were in fact concessions and renegotiations before the "same" question was asked in all cases. The referendum repeat that was preceded by least concessions was the one with the lowest initial turnout: Nice 2001 in Ireland. In that case, the changes were more declarative than legally binding and efforts focused on a better campaign. For the other repeats, the concessions were more substantive and based on the specific objections of the "no" campaigns; after the Danish referendum of 1992, there was a legally binding [under international law] document agreed by all EU heads of state, although its position within the EU legal framework was considered somewhat awkward. The Irish rejection of the Lisbon Treaty in 2008 also resulted in substantive concessions; these took a legal form similar to the solution to the 1992 Danish problem, but it was also boosted by an agreement to include a specific part of it in a future EU treaty, as to clarify its position in EU law as well. (The convenient legal vehicle that was found for the latter was Croatia's accession treaty of 2011.)
Finally, how does this relate to Brexit referendum(s)? The more concrete proposals I know about don't simply ask for a repeat (although I have no doubt the vague notion may have been publicly discussed). Instead the proposal(s) I know about were for a "confirmatory" referendum, meaning the now-concrete deal would be voted on, instead of a general/vague idea. Arguably this is somewhat different than a new referendum following concessions/renegotiation. But in either case, the public has substantially new information that it can use to answer the "same" question, which in the case of a Brexit confirmatory referendum wouldn't even be nominally the same. (Bercow would be pleased.)
And if I'm allowed an imperfect but hopefully still informative analogy: I would compare the 2016 Brexit referendum to an "informal" poll in the EU Council proceedings, which asks each member for their position in principle, at the start of a
discussion, but without binding the member to agree to whatever final legal document is produced. I have a couple of arguments in support of this: unlike the 2011 AV referendum, the law authorizing the 2016 one did not make the referendum result legally binding.
Furthermore, the uncertainty regarding the exact separation conditions (that had yet to be negotiated) give it this "agreement-in-principle" character, similar to the EU Council "informal" polls. (The analogy only goes so far, of course: there is no record kept of the EU Council's informal polls, something that's impossible to do with a nationwide referendum.) The confirmatory referendums proposed (in the amendments I know about) would, in contrast, be legally binding and also about a specific way of exiting the EU.
Finally, I will concede that the topic of repeat referendums is still controversial and does not have a lot of precedents. But even research that has been substantially more critical of the past EU referendum repeats than my position above, notes that, in principle:
A repeated referendum may be justifiable if it occurs for non-tactical
reasons or if safeguards stand in place to prevent the manipulation of a repeated vote. For
example, a repeated referendum appears warranted if legal conventions require multiple votes
for major policy changes. In a similar vein, a repeated vote may be justifiable if new facts are
disclosed on an issue central to a past referendum. Also, a repeated referendum may be
defensible if an independent, politically diverse panel oversees the conditions under which a
referendum will be repeated. If, however, a government will only hold a repeated vote when an
initial outcome contradicts the plans of its leaders, repeated referendums may, in fact,
strategically constrain contestation over policy and benefit those in power (Carson and
Martin 1999; Walker 2003). Overall, then, repeated chances may be normatively defensible
if they occur for non-tactical reasons and if mechanisms stand in place to prevent the
exploitation of referendums by those in government.
As for the main criticism of this latter research advances of past EU referendums: it is the alleged focus that the EU leaders had on "voter incomprehension" as a reason for repeat. Which I think it's true for the 2001 Nice treaty in Ireland, but less so for the other ones. The argument against a repeat due to incomprehension is that no repeats of EU referendums have been done in cases where polling suggested the public had a weak understanding of the topics, but the referendum result was "yes" (and this is illustrated with Spain).
And extending this line of reasoning, arguably one could claim that incomprehension of the consequences of Brexit (at the initial referendum) is not a reason to repeat that referendum. But there is clearly a tension between "new facts on the ground justifies repeat" and "no repeat is justifiable just due to incomprehension". There is a grey area here. Often enough a potential issue may have been mentioned in an initial discussion (or referendum campaign, e.g. difficulty of agreeing good separation terms with EU) but actual negotiations do bring new facts as to what the possible mutual agreement really looks like, and this arguably is new information.
And I know this is getting long, but here's fairly good cross-domain comparison (campaign strategy and actual concessions) of the three EU repeat referendums:
In all three of the second referendums, the Yes campaigners used two new strategies to tie the hands of No campaigners. After the initial rejection, the government sought reassurances from the EU on the controversial themes of the first campaign, effectively allowing them to ask the same question again. Having changed the context successfully, the Yes side could thereby frame the question differently. To achieve this they used their second strategy, which was to raise the stakes of a second rejection. This time the Yes side could use the risk factor, which was more available to the No side in the first rounds. Importantly, Denmark initially designed these strategies, which the Irish learned and adopted later on.
In the first rounds in both countries, as expected, the No campaign’s arguments tapped into the sensitive subjects relevant to society. In Denmark, the No side argued that the Maastricht Treaty would lead to loss of Danish sovereignty in a new United States of Europe, which would undermine or abolish the Danish currency and Danish citizenship. In Ireland during both the Nice and Lisbon referendums, the No campaigners repeatedly argued that the treaties would change Irish laws on abortion, lead to a loss of sovereignty, undermine Ireland’s military neutrality, and remove its permanent EU Commissioner.
In the second round, however, the arguments changed. The Yes side argued that Europe had listened to the Danish/Irish people and responded with legal guarantees, which were specifically on the themes raised by the No side. With the Edinburgh Agreement, Denmark would have four opt-outs in the fields of European citizenship, economic and monetary union, defence policy, and justice and home affairs. Ireland, on the other hand, gained guarantees concerning its military neutrality with the Seville Declaration after the Nice referendum, and on the Irish commissioner, competency over tax rates, abortion, neutrality, and workers’ rights after the Lisbon referendum.
In addition to the arguments on the guarantees, the Yes side emphasised the consequences of a second No vote such as potential exclusion from the EU and economic costs. [...]
As you probably know, the last issue, fear of economic impact has played a substantial role in delaying a no-deal Brexit in Parliament, even in the absence of an actual 2nd referendum.
I think the most diffcult aspect of a 2nd Brexit referendm is what to actually put on the ballot; there's the obvious issue of vote-splitting the leave side between no-deal and (e.g.) May's deal. And of course there's the issue of the voting system to use if more than two choices end up on the ballot. Neither of these have much to do with the mere referendum-repeat problem, but they do raise the "neverendum" perspective because if Parliament could not decide on how to Brexit (indicative votes) how would the public do that better? N.B. there was a poll using the Condorcet method which did declare May's deal as the winner via 2nd best-choice for most voters. But agreeing on the method to conduct a 2nd referendum is thus very likely to influence its outcome. Hence reluctance to agree to it in the first place. And of course it's easier to deflect attention from the more substantive issues by discussing it in mere democratic deficit terms.