I've done some reading up on what EU citizens are thinking about this question and their view appears to point to a demise of the institution.
The European Centre for Foreign Relations did a survey in 2019, which you can read about
here and the majority view was a collapse with 10-20 years. Only Spain had a majority which saw the bloc enduring. More worrying was the proportion of respondents across the countries who saw a chance of conflict between members
It's worth remembering that this survey was carried out at a time when Covid wasn't even on the horizon and economically, things weren't as bad as they are now. If the same survey was carried out today, my gut feeling is that the future of the institution would look even more uncertain.
Turning to the impact of Covid, another survey was done to establish how EU citizens perceived the EU's contribution to the crisis.
This Guardian article shows that the organisation doesn't come out of the survey well.
Once more, retaking opinion today is unlikely to improve citizen sentiment.
These threats to the EU would be tough to deal with by themselves but there is also the future economic double whammy it faces from the loss of the UK as a net contributor and the financial impact of the virus, which will take years to overcome.
Then add to the mix Russia's destabilising actions, America's unknown future stance towards the bloc, climate change, migration from outside the bloc and China's desire for world domination.
All in all, the makings of a bad day at the office for Ursula and co for some time to come, I think and as we have seen before, when an iceberg is approaching, human nature often kicks in and it's every man/woman/country for themselves when there is a rush to the lifeboat.