I've received another reply to signing the "don't prorogue" petition, this time from Research Briefings at "Parliamentary Procedure" It is more detailed than the first (from Government) and as well as explaining the process and its history (saying that "between sessions during a Parliament, [it] has typically lasted less than a week") it mentions the Brexit connection specifically. I am forwarding that part here for those who don't follow links.
researchbriefings.parliament.uk/ResearchBriefing/Summary/CBP-8589
The relevant bit says "Prorogation has been raised in two specific contexts in the Brexit debate.
Firstly it has been mentioned as a mechanism by which the Government could seek to get around the “same question” rule in relation to approval of the Withdrawal Agreement. In general, once the Commons has taken a decision on a question, the same, or substantially the same, question may not be proposed again in that session. A new session would have allowed the Government to revisit approval for the Withdrawal Agreement, the Commons having rejected two versions of the negotiated Withdrawal Agreement and framework for the future relationship and explicitly rejected the Withdrawal Agreement in its own right in the 2017-19 Parliamentary session.
Secondly, a long prorogation has been mooted as an option to deliver a “no-deal” Brexit. The premise of such an idea is that MPs opposed to leaving without a deal could not then use Parliamentary procedure or legislation to frustrate that outcome if it were to become Government policy. This is possible because the default position in EU law is that the UK leaves the EU on 31 October 2019 without a deal unless:
a Withdrawal Agreement is ratified;
a further extension of Article 50 is secured (which requires both the European Council and the UK Government to agree to it); or
the United Kingdom revokes its notification of intent to withdraw.
* A long prorogation has been defended by its advocates as a means of “honouring the referendum result” from June 2016. However, critics of such an approach maintain that a Prime Minister embarking on such a strategy would do so in defiance of the elected House of Commons, unnecessarily bring the Crown into a political dispute, and undermine the role of Parliament in the UK’s constitutional and democratic arrangements. *
Prorogation being a prerogative power, there is no obvious legal mechanism by which Parliament could prevent its exercise otherwise than by passing legislation to constrain it. Parliament has legislated to constrain or replace the prerogative in the past. For instance, whereas previously the dissolution of Parliament prior to a General Election was an exclusively prerogative power, the calling of an election is now governed by the Fixed-term Parliaments Act 2011.