What do you think? Does a pwBPD always do the frantic attempts to make contact thing?
Often but definitely not always. Fear of abandonment is only one of several aspects. Also keep in mind that fear of abandonment may result as well in the exact opposite behavior you describe: Leaving when first rejection happens following the logic that it is better to leave than be left.
What is almost always true is that fear and shame play a big role in the emotional life of a pwBPD. How that then is manifesting itself in the behavior - there is a really wide range as can be observed on the board
And this is why with BPD approaches that work aim at the emotional side - problems originate there and behavior is the symptom. Aiming purely at behavior is often fueling the emotional problems. That is not to say that dysfunctional behavior does not need tackling and even more importantly we need to protect ourselves adequately from its consequences.