Mail takes all mail account offline. I have duplicated this twice now. Let see if we can solve this.

Question

I see others have had this problem but I do not see a solution.  Simply put mail takes all accounts offline.  The user is unable to return them to online status.  Logging out  or restarting will not allow the reenabling of the accounts.  It takes deleting some of the files associated with mail and re entering the accounts info.  I have seen this happen only when I have high date rate incoming internet traffic and mail attempts to retrieve the mail and it may take a few times.  I download quite a few linux dvd isis so at time my bandwidth is full.  This is when it has happened every time.
Even after the traffic has ceased mail is unable to connect.  I ran disk util to see if there was a permission problem.  I disabled the firewall to see if something changed there.  Now note only mail seems affected i.e. internet usage is not.  I tried pinging the smtp server no returns. 
PING non-de-p14-imap.mail.me.com.akadns.net (17.151.226.82): 56 data bytes
Request timeout for icmp_seq 0
Request timeout for icmp_seq 1
Request timeout for icmp_seq 2
--- non-de-p14-imap.mail.me.com.akadns.net ping statistics ---
4 packets transmitted, 0 packets received, 100.0% packet loss
traceroute to non-de-p14-imap.mail.me.com.akadns.net (17.151.226.82), 64 hops max, 52 byte packets
1  192.168.10.1 (192.168.10.1)  0.589 ms  0.298 ms  0.232 ms
2  * * *
3  dtr01olvemo-tge-0-2-0-19.olve.mo.charter.com (96.34.52.217)  13.574 ms  12.964 ms  12.181 ms
4  bbr01olvemo-bue-5.olve.mo.charter.com (96.34.2.16)  13.945 ms  15.636 ms  17.989 ms
5  bbr02chcgil-bue-2.chcg.il.charter.com (96.34.0.12)  26.860 ms  23.622 ms  23.886 ms
6  prr02chcgil-bue-5.chcg.il.charter.com (96.34.3.122)  19.154 ms  18.771 ms  19.307 ms
7  17.1.148.17 (17.1.148.17)  18.822 ms  17.895 ms  19.729 ms
8  17.0.148.75 (17.0.148.75)  64.609 ms  63.703 ms  67.025 ms
9  * *
What files contain the config data for mail?  The plist file?
Before I forget this is a macbook pro running 10.9.3 OS X   Mail is Version 7.3 (1878.2)
connection doctor says  mail was able to connect to the internet( notice trace route appears okay) but then complains the servers are unreachable.
Any thoughts, things to try etc.?

Answer 1

Please read this whole message before doing anything.
This procedure is a diagnostic test. It’s unlikely to solve your problem. Don’t be disappointed when you find that nothing has changed after you complete it.
The purpose of the test is to determine whether the problem is caused by third-party software that loads automatically at startup or login, by a peripheral device, by a font conflict, or by corruption of the file system or of certain system caches.
Disconnect all wired peripherals except those needed for the test, and remove all aftermarket expansion cards, if applicable. Start up in safe mode and log in to the account with the problem. You must hold down the shift key twice: once when you turn on the computer, and again when you log in.
Note: If FileVault is enabled, or if a firmware password is set, or if the startup volume is a Fusion Drive or a software RAID, you can’t do this. Ask for further instructions.
Safe mode is much slower to start up and run than normal, with limited graphics performance, and some things won’t work at all, including sound output and Wi-Fi on certain models. The next normal startup may also be somewhat slow.
The login screen appears even if you usually login automatically. You must know your login password in order to log in. If you’ve forgotten the password, you will need to reset it before you begin.
Test while in safe mode. Same problem?
After testing, restart as usual (not in safe mode) and verify that you still have the problem. Post the results of the test.