I came across this sentence:
Accepting questions and listening. Letting others reply, even at the price of pauses, but persevering until those agree with your perspective.
What does the price of pauses actually mean?
This implies pauses (in a conversation? discussion? That's why J.R. is asking for more context) are, in principle, undesirable and should normally be avoided. The writer describes a goal which can only be obtained by allowing those pauses.
Another common phrase for this is 'at the expense of'.