When adding the item through the Portal Rest api, are you including the 'serviceUsername' and 'servicePassword' parameters? These are only available for map, feature, and image services, but that is what Portal uses to generate a new token for the services as needed.
If those parameters are already being included, I'd make sure Portal is able to successfully reach the token url for those services. The easiest way to check this to try to add one of the secured services through the Portal web application. If you login to Portal, go to My Content, and attempt to add the secured service url as an item, does it allow you to save the credentials? If not, it indicates Portal cannot reach the token url to generate a token. This is commonly caused by Portal not trusting the SSL certificate used on the ArcGIS Server. A copy of the CA certificate would need to be imported into Portal in order for it to trust the SSL certificate. More info on this can be found here.