My colleague Edwin, writing for the Exchange Support Team Central Europe blog, posted an article on accepting meeting requests with CDO. The key takeaway from the post is this:

This means that when calling the respond method on meeting updates / requests, the sequence number must be read from the request and written to the response, otherwise Outlook will not be able to match the response to the original meeting.
(The proposed solution is to read the dispidApptSequence from the original message and write this to the meeting update response before sending.)

He also points out that this requirement is spelled out in the MAPI protocol documentation, here.

Since CDO has reach end-of life, we won’t be taking a change to CDO to have it do this, so you’ll need to do it yourself. Edwin gives sample code that demonstrates how.

Enjoy!