Perhaps no one is looking at this thread anymore but I have a definitive answer for my own similar issue.
Yesterday my iPad, for no apparent reason, stopped sending mail, I tried deleting the account and adding it back only to get the error message "apple.imap.mail.yahoo.com not responding". The bulletin boards don't seem to have an answer, except that CKFROMSG on here commented about the speed of the server, and on another thread there was a comment about security settings on the poster's router.
A few days ago, concerned about the activity on my internet connection, I setup a firewall rule to match any outbound connection, allowing it to go through but logging it. This was causing the problem! No other internet use going through the router experienced any noticeable impact from the logging, however I continued to get the "not responding" message from the apple.imap.yahoo server until I turned off the logging Once I had turned it off I could add my mail account back on to the ipad and then I could connect and send mail quite happily. I turned logging on again and I could no longer send mail until I again turned it off. Seems clear what the culprit is - and I would say it's not my router!
Hope this information helps a few others out there with similar problems.