原句第二部分确实有所省略：
Doing what you like is not persistence, but doing what you don't like.
= Doing what you like is not persistence, but doing what you don't like is (persistence).
分析：Doing what you like (主语) is (系动词) not persistence (表语), but doing what you don't like (主语；其后承前省略了系动词和表 ).
