I just ran into this issue whereby emails with certain images in (not all, seemed random) resulted in a 403 Access to this resource on the server is denied! page.
I hadn’t changed anything myself that would affect this, and had been working flawlessly for years, so I contacted my host company (Krystal) and asked them. They asked me to disable ModSecurity for the domain in my cPanel. I did, ran the same tests and this time it sent and saved the draft.
The hosts then seemed to change something behind the scenes and asked me to re-enable the ModSecurity switch, and all was working again.
Posting so that this might help others with similar issues.