Some templates are created by using the WYSIWYG.  When importing an image using the image icon from the toolbar, the system uses a local link to insert the images.  The images need to have an absolute link address to appear in emails.

Here are the steps to fix this.
1. Navigate to your email template library by going to Communications > Mail Specific Features > eMail Template Library
2. Edit your template
3. Select an image and click the image icon on the toolbar.
4. Insert: https://www.kintera.com in the image file text box before /AccountTempFiles

Adding more than one image?  Repeat step 3-4 for each image.