As Labour and the Conservatives tear themselves apart over Brexit, the SNP's legendary party unity remains its greatest asset. But it is being sorely strained in this long hot summer of inaction over independence. “It's not the Brexit confusion that's delaying indyref2,” claimed the nationalist blogger Peter Curran last week, fresh from his exclusion from YouTube over the BBC's copyright ban. “It's Nicola Sturgeon who's using the Brexit confusion to delay it.”

It is unheard of for the First Minister to be openly criticised in this way and some of his followers were clearly shocked. But rather more agreed with him. Then, one of the leading figures in the 2014 independence campaign, Lesley Riddoch, weighed in with a column in the National. Had independence, she asked, been “kicked into the long grass by an FM keener on power at Holyrood than pursuing the goal she has worked for all her political life?”.

She answered her question in the negative, but the column was a sustained criticism of the SNP’s safety-first policy on independence. “If the electorate senses the keenest advocates aren’t making a bold, confident case,” she said, “it hardly bolsters confidence among the waverers.” The co-chair of the Independence convention compared independence to shooting the rapids on an inflatable raft: you just have to keep going forward because if you try to stop your vessel will capsize.

These are not isolated comments hyped up by the mainstream “yoon” media. I've been hearing Nicola Sturgeon's leadership questioned by some quite senior figures recently. This is a good thing. Too much consensus leads to intellectual and political atrophy. The First Minister remains unassailable, and there is no challenge to her leadership. But she is going to have to find something inspirational to say, or we may see the SNP’s legendary party unity finally crack in October when she gives her renewed timetable for indyref2 – or rather doesn't. The First Minister's view, repeated last week after her meeting with Theresa May, is that there needs first to be clarity on the Brexit deal, and that's about as likely as Boris Johnson buying his wife a burqa.

This is causing immense frustration in a movement that, to paraphrase Harold Wilson, is a crusade or it is nothing. Many in the party don't understand why independence should wait upon the pleasure of a dithering and divided Tory government. What about the “triple lock” mandate: the Holyrood election victory, the parliamentary vote for a referendum and the majority in the 2017 Westminster elections? This mandate is a perishable commodity. And anyway, say commentators like the influential independence blogger James Kelly, the SNP has a “moral duty” to call an independence referendum to honour the commitment in last year’s manifesto.

Curran and Kelly argue that it is futile to wait until there is a sustained lead in the opinion polls for independence because that movement in public opinion will only come as a result of political leadership. When the last referendum campaign was launched by Alex Salmond, support for independence was stuck at 25%. Yet, by the weekend before the referendum ballot, some polls showed Yes neck and neck. Support for independence today is 45% and with a powerful campaign, they say, it could easily reach 60%. Why is she not out there already, leading from the front?

The First Minister has not deigned to appear at the recent independence marches, in Glasgow and Inverness – some of the biggest ever. She does seem happy to lead LGBT+ marches though – which is all very well, but her supporters would also like to see her out on the streets in The Cause. The SNP doesn’t endorse the All Under One Banner organisation, but if Sturgeon were to take over and lead these independence rallies, they would surely attract even greater numbers, like in Catalonia. What has she got to lose?

However, Sturgeon is not a populist, and dislikes angry demonstrations and political theatre, especially if it involves figures like the former SSP leader, Tommy Sheridan. She didn't intervene in the extradition of the Catalan nationalist, Clara Ponsati. She doesn't subscribe to Twitter storms, or support campaigns against bias in the BBC. She hasn't been giving much encouragement to disruption at Westminster over the Brexit “power grab”, though she has spoken strongly against it in Holyrood. The First Minister sometimes gives the impression of being more interested in policy than the passions of independence, and delivering on things like educational attainment targets – a thankless task.

However, Nicola Sturgeon has very good reasons to be cautious about insurgent politics, since she tried it only last year with disastrous results. For an SNP leader, there's nothing more humiliating than calling an independence referendum and then calling it off again, or “resetting” it. As a result of that miscalculation, the SNP lost a third of its MPs in the subsequent general election, including those of her Westminster leader, Angus Robertson, and the former leader, Alex Salmond. She's not going to make that mistake again, and wants to see support for Yes heading in the direction of 60% before she acts. She realises that another failed referendum would kill independence stone dead – as it did in Quebec.

So what is she going to say in this crucial conference speech in October? She can't just say that she'll come back next year, because politics will have moved on and Britain will be out of Europe. Well, one thing she could do is call for a different referendum: a People's Vote on Brexit. Nicola Sturgeon has been edging closer to endorsing a think twice referendum on Europe, but to the frustration of some of her closest advisers, she has not gone the distance. This could be the moment.

If the First Minister were to declare support for “Brexyref2” she would at least be seizing the political initiative, and giving her party something concrete to do. There is an aching vacuum in politics right now because Labour has refused to support any repeat referendum, or even soft Brexit. There's already 60% Scottish support for remaining in the EU and this can only grow as the chaos deepens this autumn and winter.

Once the UK leaves the EU, Scotland will be out of Europe and Scots will lose their rights and privileges of EU citizenship. It also makes independence more problematic. The Irish border issue moves to the mainland, because if an independent Scotland tries to rejoin the European Union it would mean a hard border with England. This could make it that much harder to persuade middle Scotland that it is worth the trouble of leaving the UK – especially after witnessing the trouble caused by leaving the EU.

Nicola Sturgeon can legitimately argue there is no point in calling a referendum on Scottish independence now because the voters are simply not in any mood for one. Their minds are filled with images of stockpiling of food and medicines after a no-deal Brexit. But they could be mobilised to reverse or freeze Brexit. It wouldn’t satisfy the go-for-it tendency, but it would be better than sitting around doing nothing. And if it fails, it makes the case for self-government that much stronger.