I think that the delayed response time on email replies from Continental is occurring regardless of the topic.
It took 12 days to get a reply from CO for Mrs_dergon's last attempt to contact regarding a bagge issue.
I had to cancel a ticket in mid april. It got fubar'd by the elite line rep. So contact to CO via email on 4/24. No reply. Follow up 5/1 .... still no reply.
I don't think it matters whether you're emailing regarding Copa issues, baggage, dead dogs, screwed up reservations, or what have you ...they're just slow to reply electronically.