First of all, many (almost every) email client block pictures to be displayed and ask users an explicit consent to show them. Please verify that this is not your case.
Furthermore, please make sure that you are including the URL of the banner as an absolute path. For example, if your domain is http://www.mydomain.com and the banner you are including in your template is banner.jpg, located in the /images folder, you have to write it as follows:
<img src="http://www.mydomain.com/images/banner.jpg" />
If you write it as a relative URL:
<img src="/images/banner.jpg" />
of course you will be able to see the banner while editing the template and the email, but the user receiving the email won't see it.
Please let me know if this helps.