Closely related to: What would be the subject of a second Brexit Referendum?
Currently, there is discussion about a possible second referendum fueled by Labour, and there seems to be the publicly voiced conception that Lord Kerr (who is regarded as being somewhat authorative) sees it perfectly possible that UK revokes its Article 50 notification, and this just works out.
If, having looked into abyss, we changed our minds about withdrawal, we certainly could - and no-one in Brussels could stop us.
That's quite problematic, considering that not just the UK has looked into abyss, but the remaining states have as well. Even assuming it was technically possible to simply stop Brexit now, it couldn't possibly work that way practically, since it would serve as a precedent for copycats invoking Article 50 over and over again regularly, every time causing billions of damage to economy and causing a massive destabilization of the entire union, effectively being a means of blackmailing co-member states. So, from a purely practical point of view, this is actually not something that should be remotely possible.
Also, back in 2017, the EU Commission explicitly stated earlier the same day UK filed the notification that whether or not to give notification is everybody's discrete decision, but the notification is a do-once point-of-no-return thing. This was well-understood by all parties.
That point of view does seem to make sense, too. After all, invoking Article 50 and giving the notice is akin to telling your wife: "I slept with your sister, and now I want the divorce". You cannot take this back, once you said it.
Now, looking more closely and not taking one sentence out of context, it seems like Kerr himself indeed is not as absolutely positive about it as it may seem, either:
The European union is a union of democracies. If this Parliament asked – and our Government conveyed our request – for an extension, in my judgement it would certainly be given.
Now wait a moment. He said "ask", not "inform" or "tell". Ask implies the other side can say "no". Also, he said "extension", not "reversal". Also, extension would (likely) be given, in his judgement.
So that doesn't look quite as confident, and indeed suggests that UK cannot just unilaterally revoke Brexit. Or, at all.
Rather, it looks like they might kind of ask for mercy (sorry for the slightly provocative wording) and if the remaining member states decide so (which Kerr believes would happen) then an extension would be granted. Extension, not reversal. That's a totally different thing, altogether.
Time to look what's actually in that infamous Article 50. There is nothing in there that I can see which suggests it is possible to revoke at all. In my understanding, the wording, in particular sentence (3)
... failing that, two years after the notification [...] unless the European Council, in agreement with the Member State concerned, unanimously decides to extend this period
suggests exactly what Kerr expects in his second quote: The remaining states would have to decide, unanimously, that they're happy with granting an extension (...to the exit negotiation period). Assuming only a single member state disagrees, bad luck, the lights just go out end of March.
Of course, UK could, following Brexit, apply again to become a member state according to Article 49. Indeed, Article 50 explicitly states that. However, this obviously wouldn't just work, it would be subject to fulfilling all of the basic conditions, plus some. Also it would be subject to member states agreeing. Surely, member states would expect to get "paid" (one way or the other) for the economic damages they've had from the uncertainity caused by Brexit, it seems unlikely they'd just shrug and move on.
So, considering that a second referendum and attempting a full U-turn half a year before Day X would be most devastating in terms of credibility (both internally and externally), but also stopping the Brexit does not seem to be possible at all ("extension" does not mean the same as "reversal"), what would be the point in holding such a referendum in the first place?
In my opinion, at this point in time, it can only make things worse, not better.