Is there a continuous cost for having fanout keep the connection between a client and the origin alive?

Fanout is mainly used to keep connections between clients and origin servers alive. Would I be charged by how long this connection is kept open. Or is it a one time cost? Any insight into the pricing model would be much appreciated!

You are charged by connection duration, among other things. For example, if you have 5 connections at the same time, and each lasts 10 minutes, this would be counted as 50 minutes towards billing. See: https://docs.fastly.com/products/fanout#billing