When attempting to download a component through a conan proxy repository the client repeatedly requests a password. The Nexus request.log records 401 authentication failure responses.
If Anonymous access is not enabled, you will need to enable the Conan Bearer Token Realm (via Administration → Security → Realms).
After this, logging in with the "conan user" command should work:
Documentation for configuring conan proxy repositories is available here: https://help.sonatype.com/repomanager3/formats/conan-repositories