I am using Fauxton in a test environment to replicate from our test server to my local server. I logged in to the test server in another browser tab, but replication still fails despite the cookie being there.
The solution is to prepend your username and your password to the remote replication URI:
https://user:[email protected]:7984/mydb
See http://wiki.apache.org/couchdb/Replication#Authentication for more information.
(This approach should be reviewed or avoided in a production environment.)