Alexandra, hang in there. I don't think his not answering the e-mail necessarily has any significance about whether he wants to continue with you in the future. He could be simply overwhelmed with the new baby. Is it his first child? Speaking from experience, when my first baby was born, I don't think either me or my husband slept much the first couple of weeks. We were totally sleep deprived and not thinking clearly. Maybe he hasn't even checked his email since the birth. I really think you and your T are going to be fine, and your alliance will survive this.
Could you do something to get your mind off this for a while? Immerse yourself in your work? Go away for a trip? Find a new lover?

Anything?