It's been halted by the numerous suggestions that the referendum may simply be ignored or the result otherwise blocked. It's a lose-lose scenario, since shit will likely hit the fan again once one of the two cans of worms is reopened.
I read a few headlines that said Parliament confirmed the referendum would be honored. If the next PM ignores the outcome all together, that would be extremely disturbing. A mockery of democracy.
Parliament hasn't confirmed anything. It is the common opinion that the vote must be respected, but no one actually wants to go ahead and start putting it in motion. Legally, it needs to go to a vote*, which it hasn't yet, and the majority of MPs support Remain. I agree that it would be super-controversial if they blocked it, but it's very much a possibility. That's what I meant by "two cans of worms" - either we fuck ourselves up by actually going the Brexit route, or we fuck ourselves up by going the Remain route and dealing with the unrest that follows.
If the next PM is Theresa May, as is looking more and more likely, I wouldn't be surprised if she deferred the issue by calling a general election - in which case it would all be up in the air. The Liberal Democrats (not a party many take seriously these days, but still one of the bigger parties out there) have already pledged to ignore the referendum result if they happened to win. If Jeremy Corbyn is ousted, it's not entirely unlikely that Labour might do the same.
* - that claim is disputed, but the majority of experts seem to agree. Then again, this country has had enough of experts!!1!