Around the Firefox v29 timeline, Mozilla changed the authentication mechanism for Firefox Sync to use Firefox Accounts. Consequently, the setup method for custom self-hosted Firefox Sync servers changed (note that my guide has yet to be updated), and for a few releases Firefox for Android did not support the new model.
Fortunately, custom Sync server connectivity has been restored as of Firefox for Android version 33. The full guide (including an add-on which enables custom sync server addresses) can be found on Nick Alexander’s blog.
Note that if you’re using a “non-standard” port for either your custom Sync or Firefox Account servers, you’ll run into the bug described at https://bugzilla.mozilla.org/show_bug.cgi?id=1046020, which as Nick says manifests itself as an authentication error. The workaround suggested is to use Firefox Beta, which works for me.
It’s terrific that Mozilla continues to offer its users the choice of self-hosting their solutions.