Are you examining the return value of Smtp.SendMessage method?
Have you ever had a similar problem?
No, never.
we enable logs on the client dll, but no error appear
In such case it seems that your SMTP server accepted the message and it is now responsible for delivering the message or generating a failure report.
Why do you think the problem is with Outlook 365? Maybe it's your SMTP server, that is swallowing the messages.
Are you sure you're not treated as a spammer?