I don't have good solution, but I think this is connected to performance and overloading: if you set the first email task into something lighter, like sending only few pictures, or smaller pictures, it might allow the second task to perform better.
I don't have good exact solutions, but if you play with those kind of settings you might find out something.
I have similar: if I send lots of pictures through the email, then the FTP transfer does not work properly. But currently I have done Sir of compromise. One thing that might mean something if you use the same _media_ for both events or not: try using different sets if it helps?