To get the logs, which are by no means simple even for a second level support to decipher but to get them anyway and post them launch the conneciton doctor, click show details, followed by check again.
There will be a lot of text, especially with four active accounts. It's best to post them if you find a problem while only one email account is enabled.
I have a better idea than what I propose with the exception of giving us logs for the one bad account.
Let's use some isolation, simple tests and observations.
1) Go to Mail>Preferences>accounts
2) Select one account at a time (you should see 4 on the left side)
3) Click the Advanced Tab
4) Remove the checkmark "Enable this account"
5) Do the above to 3 of you4 accounts.
-don't worry, your emails are all still there but they hide as a result of removing the tick next to "Enable this account"
-Close the mail preferences window and save
6) open connection doctor
7) All green lights?
8) If yes, then send an email to yourself
9) does it go out and come back?
10) if yes then this account is fine
You can now go back to the beginning of the steps, and disable this good account and enable one of the other 3 acocunts that we had disabled. Do one account at a time. Eventually you should find the culprit through connection doctor or sending / receiving email actions.
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Also, what do you mean by loactions?
I use the iMac in the UK and in France (La Bell France right now). Each time I change location I have trouble with mail.
Do you mean physcial locations? Does a different wireless or wired network produce different results? Is this what you are meaning?
Let me know, I'll chime back as soon as I can and do report back on your findings using the method above to check on an account by account basis which in itself is atypical of me to request but the issue is hard to figure out. The locations bit, for me anyway, needs some more detail.
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Also, this extremely well put together article can prove most useful! …http://support.apple.com/kb/TS3276?viewlocale=en_US&locale=en_US
Incidently, this link does mention location, here is what Apple support has to say on location and how it can affect email.
Yes, I am connected from a new location
- In the Mail Connection Doctor, double-click the row that has a red dot next to an account name containing "smtp".
- Click the Advanced tab.
If your Internet service provider and email service provider are the same company, and your SMTP authentication is set to "None", you may be able to send email only when you are directly connected to the Internet via your Internet Service Provider.
Kind regards
Alex