Consider, if you will, this common-enough opening to an everyday scenario.
Boys meet girl, boy likes girl, girl likes boy. Boy wants relationship, girl wants friendship. Happens all the time, yes? Happened to you on one side of other I'd wager.
Anyway, I've known people who've reacted (or the person whose interested in them has reacted) in three different ways:
In Scenario A, despite the rejection the guy still hopes something will happen. He persists, eventually the girl's won over, they get into a successful relationship.
In Scenario B, despite the rejection the guy still hopes something will happen. He persists, the girl is never won over and the guy spends months, perhaps even years, wasting time pining over a girl he'll never ever have.
In Scenario C, despite the rejection the guy still hopes something will happen. He persists in a somewhat obsessive manner, girl is rather freaked out and understandably does everything she can to avoid him on all future occasiosns.
Obviously Scenario C we can discount C to some extent as it comes down to the guy's behaviour and manner of approach as much as anything.
But basically the questions we're leading to here are:
1) When does persistence become desperation?
2) How does one judge when to be (politely and gently) persistent and when to walk away?
3) Is the biggest difference between successful and failed persistence the persuasiveness of the guy or the extent to which girl desires to be won over by said guy?
4) Insert any other question you fancy.