per-: through, completely
sist: derived from Latin "sistere", meaning "stand"
-ence: the action of doing something
So persistence means:
The action of standing through (the whole time or process).
If someone wants to stand through the whole process of something, he/she must want to finish it completely. So persistence means "the action of continuing to do something, although it is difficult, or other people oppose it".
Evolution of usage
The action of standing through (the whole time) is a necessary requirement for success.
The action of persisting is a necessary requirement for success.
Persistence is a necessary requirement for success.