When using an authenticated proxy service with SAML, the authentication process requires a web-based login — typically a browser window where you enter your username, password, and possibly complete MFA.
However, non-browser-based applications (like eM Client desktop app or background services) don’t have a built-in browser interface to handle that SAML login flow. Because of this, they cannot prompt for or complete the authentication process, and the connection fails with the error: RetrieveLicenseXml failed 

If you instead use one of the following setups, everything would work normally:

In short, SAML-authenticated proxies require a browser UI, which is why non-browser apps cannot authenticate properly under that setup.