Mac OS 10.7.5 Mailaccounts offline after switching imac on. Second start helps sometimes. Explanations?

Question

Hello friends,
after loading all imaginable updates for OS 10.7.5 my (two) mailaccounts are offline, showing the triangle with exclamation mark. Sometimes it helps to click at one of the triangles and acknowledege to go online. In most cases I have to start the imac for a second time. Can anybody explain why this happens?
Juergen
<Edited by Host>

Answer 1

Each account will have 2 entries/attempts/dota, one fot Incoming, one for outgoing(SMTP), so all is good except outgoing on both.
Is the iCloud SMTP... smtp.mail.me.com, or... smtp.me.com?
If the later...
Do not delete the old account yet. sign up for an iCloud account if you haven't.
I understand .mac mail will still come through. Do not delete the old account yet.
You cannot use .mac or MobileMe as type of Account, you have to choose IMAP when setting up, otherwise Mail is hard coded to change imap.mail.me.com to mail.me.com & smtp.mail.me.com to smtp.me.com, no matter what you try to enter.
iCloud Mail setup, do not choose .mac or MobileMe as type, but choose IMAP...
On second step where it asks "Description", it has to be a unique name, but you can still use your email address.
IMAP (Incoming Mail Server) information:
    •    Server name: imap.mail.me.com
    •    SSL Required: Yes
    •    Port: 993
    •    Username: [email protected] (use your @me.com address from your iCloud account)
    •    Password: Your iCloud password
SMTP (outgoing mail server) information:
    •    Server name: smtp.mail.me.com
    •    SSL Required: Yes
    •    Port: 587
    •    SMTP Authentication Required: Yes
    •    Username: [email protected] (use your @me.com address from your iCloud account)
    •    Password: Your iCloud password
Also, you must upgrade your password to meet the new criteria:  8 characters, including upper and lower case and numbers.  If you have an older password that does not meet these criteria, when you try to setup mail on your mac, using all of the IMAP criteria listed above, it will still give a server error message.  Go to   http://appleid.apple.com         then follow directions to change your password, then go back to setting up your mail using the IMAP instructions above.
Thanks to dpepper...
https://discussions.apple.com/thread/3867171?tstart=0