I have tried the following sample but could not reproduce the issue. Your sample message file is required to analyze the problem and provide assistance accordingly, therefore please share the sample file for our testing.
MailMessage message = new MailMessage("user@gmail.com", "to@gmail.com", "Test Subject", "Test Body");
MapiMessage mapi = MapiMessage.FromMailMessage(message);
Console.WriteLine("Old body:");
Console.WriteLine(mapi.BodyHtml);
mapi.SetBodyContent("This is the new content.", BodyContentType.Html);
Console.WriteLine("New body:");
Console.WriteLine(mapi.BodyHtml);
Thank you for providing the sample file. It is observed that body is updated and displayed fine by Outlook, however Aspose.Email does not show it properly. This issue is logged under Id:EMAILNET-38827 for further investigation by the product team. You will be automatically notified once any update is received in this regard.