The EU will be replaced by a similar collaborative organisation
The problem lies with the institutions, rather than the EU itself.
The European Union will not last, as EU Member States are increasingly at odds with the European Union's institutions. The raft of issues the EU faces from the Eurozone crisis, the migrant crisis, and Britain's exit will eventually lead to the institution's collapse. Of course, it will remain necessary for European countries to collaborate and their leaders to meet regularly. Therefore, the collapse of the European Union will lead to its replacement with a similar body, even if it is not as powerful.
Increasingly stuck between two global super-powers in the USA and China, European countries will continue to support the existence of the European Union as a counter-balance. Recognising that as individual states they cannot compete alone, as well as the economic and political cost they would incur if the European Union collapsed, Member States will elect to pool sovereignty where necessary.
[P1] EU Member States are at odds with EU institutions. [P2] This tension will lead to the EU being replaced by a different sort of organisation.
Rejecting the premises
[Rejecting P2] The EU will be able to weather these challenges.