Here's why:
* It refers to a quality or concept: Persistence is the quality of continuing to do something despite difficulties. It's not a thing you can count.
* We don't use plural forms: You wouldn't say "persistences."
* It uses singular verb forms: "Her persistence was impressive."
However, there are situations where "persistence" can be used in a countable way:
* Specific instances: You could talk about "the persistence of a rumor" or "different forms of persistence." Here, it's referring to specific occurrences of persistence.
* Figurative language: You might say "He has a persistence of vision."
Generally, though, treat "persistence" as uncountable.