Looking at the account, I think this is r-families.com.
Are you sure that this is a recent phenomenon? Because this issue sounds like exactly like what you would expect from this security system.
In short, it’s normal that images hosted with us don’t work elsewhere, because we provide a website hosting service, not a file sharing service.
“Can’t establish connection” could mean anything. I know that FileZilla can produce quite detailed logs, but I’ve never used CoreFTP.
Can you please explain this in more detail? Which URL did you use to access the files directly, what did you see before and what do you see now?