Dynamo store bindings between sessions

Bindings are actually stored in the DYN if you save the file after running it, not just leveraged in a single session.

This forum post should get you squared away: Element Binding in Revit

This AU session should help you get a better understanding on the issues at play: Getting the Good Stuff Out of Pandora’s Box: Element Binding in Dynamo for Revit | Autodesk University