missing messages HTC One
I think I may have similar symptoms. On some emails with attachments, none of the message gets through (just an email with subject and attachments shows up, though on my laptop I see an accompanying text message).
Phone NOT rooted;
App: the email software that comes with the phone.
Type of email account: pop 3 account using Spamarrest to block spam.
So I seem to be getting all my email, but some that come with attachments are hiding an accompanying text message. The entire messages make it to my laptop.