In order to save credentials, you need to add the service as an item under My Content. When you enter the service url, you should be prompted to enter credentials and see a radio button to select to save the credentials. There are a few scenarios where you will not see the option to save the credentials:
1. If the service is secured with web-tier authentication (IWA, PKI, Basic, etc.), you won't be able to save credentials.
2. If the service is inaccessible by Portal (ex blocked by a firewall or proxy configuration), you won't be able to save credentials.
3. If Portal does not trust the SSL certificate used by the Server web adaptor, you won't be able to save credentials.
Once the item has been saved, you'll add the item to the web map rather than the service url and you should not be prompted for credentials.
Jeff