The coronavirus crisis runs rampant throughout Europe, and many officials have called for pan-European coordination. Unfortunately, however, actions to combat the pandemic early on were fragmented and weak. The EU Commission is expected to "unveil a recovery plan to boost the sickly economy," including the creation of an EU bond to raise money for a €500 billion fund.
However, this proposal will likely by opposed by several other EU nations, including Austria, Denmark, the Netherlands, and Sweden. As a result, support on the plan is split, thus weakening the arguments for the EU, an organization comprised of countries with opposing interests.
Meanwhile, citizens of their respective countries have increasingly become disillusioned with the EU as the coronavirus pandemic went on. Around 61% of respondents from Italy have said that the pandemic has weakened the EU compared to 40% in Germany and 47% in France. A high percentage of people also believe the EU has not done enough to help their country (70%, 60%, and 57% for Italy, Germany, and France respectively). 
With the EU not offering enough fiscal and medical aid to the countries most burdened by the coronavirus, there isn't really a case for the EU to continue on as an entity.
Even more concerning is the lack of solidarity among EU members. The EU was established with the base goal of building up solidarity among its member states. However, the coronavirus made it clear that solidarity is little to nonexistent among the states. When the coronavirus first began to spread internationally, member states closed down national borders well before imposing domestic policies such as "social distancing," which are much more effective in slowing down spread of the illness. The EU's single market was also damaged as exports of personal protective equipment (PPE) were banned. The export ban was eventually lifted, but only after China and Russia delivered PPE to Italy before any EU nation did. 
This series of events only shows the cracks and weaknesses within the foundations of the EU.