What result do you get from the BE_GetLastError function? Have you also looked at using BE_Curl_Trace to look at the details?
Most likely it's to do with authentication or SSL, and may require that you use a different port or some other authentication options.
I just signed up for your sponsored support, so I will send more into to the help centre.
I could send mail through plain text authentication server as
BE_SMTP_Server ( "user%40mydomain.com:passwordASIS;auth=PLAIN@smtp.mydomain.com" ; 587 )
but the mail don't have charset in Content-Type header. There might need some option.
(my password have only alpha-numeric chars, it may need url encoded, like @ in username is encoded)
Thanks for great plugin.