As the SNP meet in Aberdeen for their annual conference, the party’s position couldn’t look stronger.

They command a supposedly-impossible majority in the Scottish Parliament. They have successfully passed the baton of leadership to a new First Minister who currently greatly outshines her predecessor. They won 56 of Scotland’s 59 Westminster seats in May.

Yet despite this seemingly impregnable position, storm clouds are gathering. The party has already lost an MP, after Edinburgh West’s Michelle Thomson lost the whip due to investigations into possible mortgage fraud.

Other Nationalist MPs are already under scrutiny, be it for nepotistic hiring practices or allegedly overseeing abuse in a care home in the 1990s. The downside of a surprise landslide is that many candidates selected for ‘no-hope’ seats weren’t thoroughly vetted, and the SNP is reportedly frantic about what else might come up.

All this was before Peter Murrell, the SNP’s chief executive and Nicola Sturgeon’s husband, possibly implicated himself in unlawful collusion between the party and another separatist group, Business for Scotland, during the referendum.

This string of bad news appears to finally have scraped off some of the SNP’s previously impenetrable Teflon coating. With six months to go until next year’s crucial Scottish elections, there’s a growing sense that the only way for its stratospheric poll lead to go is down.

But there are deeper, structural challenges facing the SNP which might prove more serious in the long term.

It can’t be stressed enough, if you’re only familiar with the post-referendum SNP as a party of the left, just how broad the current SNP coalition is.

Prior to the huge influx of left-wing, disengaged ex-Labour voters from the central belt during the referendum, it was the de facto centrist, anti-Labour option. Most of its seats voted Tory in the 1990s. In addition to tactical Tories many genuine nationalists are of the commercially-oriented, cut-taxes-to-compete sort.

Currently, the spend-only setup of the Scottish Parliament means that the Executive doesn’t need to make decisions that displease one group to please another. But with Holyrood set to get substantial taxation powers, that’s no longer the case.

Worse, for the newly-minted red SNP, is the news that according to the Times (£) Scots aren’t willing to countenance tax increase to counter austerity.

That Scottish and English attitudes aren’t very different has been apparent in issues polling for ages, but the new devolution settlement may finally see the usual political rules reimpose themselves north of the border.

This skewers the Nationalists on the horns of a dilemma: hold to their current course and risk shedding their centre-right, anti-Labour base, possibly to Ruth Davidson’s rejuvenated Conservatives.

Tack to the centre, and they might fatally alienate their shiny new activist base and, more important still, terminally disenchant the left-wing voters whose defection from Labour put independence within reach last year.

Independence, incidentally, is the other issue which could cause Sturgeon and her party serious grief.

Being the party of power in Scotland will also inevitably mean that the SNP is going to start, if it hasn’t already, attracting many people who aren’t particularly enthusiastic about independence.

Such members will be happy to support the party leadership, who are currently trying to downplay the prospect of another referendum. But much harder to reconcile will be the true believers, who will not be happy that a debate on ‘IndyRef 2’ has been cut from this year’s conference programme.

After the SNP defied all predictions (including mine) in order to thrive, rather than decline, after their referendum defeat one hesitates to prognosticate on their fate.

But it does seem that their current, extraordinary position hinges on a very particular set of circumstances which conspire to minimise the pressure placed on the huge internal tensions in their support base: the prospect (or at least hope) of a rematch to maintain the party’s formidable discipline, and a Santa’s workshop Parliament that doesn’t need to make difficult tax decisions.

Neither of these conditions is going to last forever, and both look like they may not actually last for long.

Learning from Quebec, the Nationalist leadership know that a second referendum defeat would likely be much more permanent, even if the result was closer. So they won’t call one unless they can win it. If they postpone it, they annul the first condition.

Without the distorting influence of the constitutional preoccupation, this would leave the SNP with nothing to talk about except their domestic record and policies. The former isn’t very good and the latter, as mentioned, will deeply divide a party united by little save separatism.