mailbox not downloading images in e-mails

Is there not a "Load images" icon at the top right of the message which you can click on?

 

You most likely have image display turned off in the Mail preferences by default. As already mentioned, you can click the button in the top right to turn them on with each individual email if you don't want to change the preferences.

The other possibility (which is impossible for me to guess without knowing exactly how the email is being sent) is that the email itself is nothing more than an HTML page being sent via email and the images actually live on a server. If this is the case, it's possible that the images have been removed or the path has changed on the server.