The phrase "can't persist" is correct and usable in written English.
It can be used when discussing the inability to continue or endure in a particular situation or context.
Example: "Due to the overwhelming challenges, I realize that I can't persist in this project any longer."
Alternatives: "cannot continue" or "unable to endure".
Fascination can't persist, either.
We can't persist in thinking of these things as free".
Perhaps it's appropriate to take things one step further: if a liberal order can't persist without policies that ensure the gains from growth are broad-based, then maybe a liberal order can't persist without the institutions that provide the political muscle to ensure such policies are adopted and sustained and that may include strong labour unions.
So we were quiet again, the fifty of us, we were fearful again, but it didn't last too long, because fear can't persist unless you have at least a little evidence to sustain it.
Whenever there is an authoritarian coup rooted in an irrational ideology, well-meaning people insist that it can't persist because the results are going to be so obviously bad for the people who believe in it, whether it's the theocratic revolution in Iran or the first truly autocratic Administration in America.
An economy can't persist for very long by buying its own debt with printed money.
But insect wings are in motion, with flapping and vibrations, resulting in churning and eddies, and the misconception that physics says "bumblebees can't fly" persisted throughout most of the twentieth century.
The Oxitec mosquitoes, however, are designed to have negative traits that won't persist since they all die; it's a dead-end system that can't be picked up by other species.
Of course, the magic couldn't persist.
That sharp uptick didn't persist.
