If Google and MS Exchange were to implement this, it really would shift our relationship with e-mail into a much more mature and intelligent place. We’ve had e-mail for ages now, we really should have moved on more than we have.
Seven email problems – one solution, I think
You can have your inbox set to destroy email after a certain time period. The sender is alerted to the fact that their email will be destroyed after xxx number of days, so if no response has been received in that time, assume email bankruptcy on behalf of the receiver, and use a different method to communicate your demands/thanks/wishes/offers.
You can also send time limited email – if the receiver has not read the email by a certain date, it becomes irrelevant or too late, and so the email is deleted, so that saves the issue of protracted apologetic comms that are dull for everyone involved. You could set this email to alert you when it is deleted unread, just so you know, in case you want to pursue the issue on a different medium.