According to this tutorial in 6.0 you can set the scheduler to sync assets automatically, AEM 6.0 Forms Help | Migrating LiveCycle assets to AEM forms however after finding what appears to be the equivalent bundle in 6.2 ("FormsManager Addon Configuration") and setting it a time it still does not sync automatically.
Manually syncing does work if you go to /lc/aem/forms and use the create button to manually sync files from workbench. Is there something I am missing that the scheduler requires to function?
That synchronisation handler might fail if you have changed the administrator password in Livecycle and not updated the Livecycle SDK configuration. Check the error.log in the OSGi side as well as the JEE server.log and see if you are getting any authentication errors.