Could it be possible to have an icon to say that the E-Mail you have sent has been read or unread by the recipient?
To do this when a message is sent to the recipient from Myheritage to say you have a message, you will have to exclude the content of the message and then the person would have to go to the inbox to read the message.
The reason I ask is, you would know if the person is active on the site or not using the email address associated with the site (or just ignoring you)
I will pass the idea on to the development team for consideration.
In the meantime, there is not much that we can do regarding a member that is unresponsive. What I can suggest to you is to go to that persons profile and add a comment to their profile. They will then get an e-mail, and perhaps they will be more likely to get in touch with you.