Firstly, to address the example of the COVID-19 pandemic, and its effect on the popularity of Donald Trump; the level of correlation between the performance of the economy and US presidential popularity is well studied. For example, LSE research in 2013 found that presidential approval is highly sensitive to changes in the share index:
A positive change in the index, when controlling for other relevant
factors, on average produces an increase in the President’s approval.
Interestingly, the effect is even more pronounced when we look at
market acceleration or deceleration. When the market is growing at an
increasing rate, voters reward the president, but when growth is
decelerating, the president is punished.
You are right that President Trump's current opinion polls would seem to buck this trend, as the stock market has plummeted, with the Dow Jones crashing around 8000 points since the end of February, while the President enjoys record high approval ratings of 49% according to Gallup. However, I would argue that instead of an indication that these two measures are no longer intrinsically linked, they are rather an exception to the rule, precedent for which already exists.
We can, for example, consider the performance of the stock market in the wake of the 9/11 attacks, with the NYSE and the Nasdaq closing for almost a week, the Dow Jones falling 14%, and the NYSE market falling by 7.1%, a record at the time. Clearly in normal times, this would have led to a dramatic fall in presidential approval. However, as you note in your question, President Bush's approval rating soared to around 90%, the highest ever for a US president, and would go on to gradually lower over his tenure as President.
Another example might be the Gulf War in 1991. Although this took place in the middle of a recession, which had lowered the approval of President Bush Snr., his victory in the crisis gave him record approval ratings. This lead was, however, squandered over the next year, as Gallup puts it: "Americans' attention shifted from the Persian Gulf to the struggling U.S. economy". He would, of course, go on to lose the 1992 election to Bill Clinton.
It seems, therefore, that rather than this incongruency representing a break from the established conventional wisdom that presidential approval, and as a result, US political outcomes, mirrors the stock market, it is at least at the moment a reflection of previous examples of the 'rally around the flag' effect that you note in your question. Whether or not Trump's approval rating continues to stay at this high level will depend on how his response to the crisis is judged by the American public.
Secondly, to evaluate the scope of your question more generally, there is a growing body of research which seems to support your notion that the aforementioned link between the performance of the economy and the electoral outcomes of incumbent politicians is becoming weaker, at least in the US.
For example, the NYT conducted a survey (notably before the current pandemic) weighted to match the demographic profile of the population of the United States, in which public opinion regarding Trump's handling of the economy was tested. The full results can be found here. Their analysis suggests that:
Economic conditions have historically been among the best predictors
of presidential elections, and models based on those patterns suggest
that Mr. Trump would be favored to win re-election if the economy
remains more or less on its current path through Election Day. But it
is unclear whether historical lessons hold in an era of heightened
In particular, SurveyMonkey, who conducted the poll, note that
When asked which political party in general does a better job handling
the economy, the public is locked in a 45-45 deadlock. Republicans
overwhelmingly (95%) favor the Republican party, while Democrats
overwhelmingly (88%) favor the Democratic party. Independents are
split, with 39% favoring the Democrats and 36% favoring the
It would seem according to this research, that although "Jobs and the economy" remains the most important issue for the largest proportion (24%) of the survey participants, their other partisan beliefs are unlikely to shake their party loyalty in the wake of a change in economic fortunes.
In addition, 538 has a great article on this, which I won't go into too much detail on because this answer is already pretty long, but in particular, Silver notes that:
In particular, we don’t have enough data to make overly specific
claims about the economy. That is, any time you see what you might
call a “magic bullet” claim, such as that second-quarter GDP is
crucial or that per-capita disposable income is the key economic
variable, you should be wary.
Although he also echoes the misgivings of the NYT article, that partisanship could dull the response to a recession, he maintains that the performance of the economy is still very important to the outcome for the incumbent party - "The better off America is by November, the more likely he is to be re-elected."
In conclusion, then, although there is evidence to suggest that the conventional link between the economy and the fate of incumbent officials is weakening due to increased polarization and partisanship, the link is still undeniably extant. While in this specific case around the COVID-19 pandemic the incongruency can perhaps be explained by the 'rally 'round the flag' effect, it seems likely that the ultimate fate of Trump's 2020 campaign will be defined by his response to the pandemic and the underlying economical issues over the coming months. It is still far too early, in my opinion, to write off our conventional knowledge based on a few opinion polls conducted during a crisis.