U Verse and Mac Mail--the ongoing saga of intermittent connectivity-Please Help!

Hi, I've just joined this forum in order to sort out an issue that is boggling me since I switched from ATT DSL to U Verse two weeks ago.  Bear with me, please.....

I have a Mac Mini, and use MacMail for my e-mail with SBCglobal.net address, which is really an ATT address, and has been for years.  I had very, very rare mail issues with DSL, but since switching to U Verse, it's been a nightmare.

I've read this thread  http://forums.att.com/t5/Features-and-How-To/Thunderbird-third-party-email-accounts-setup-PLEASE-HELP/td-p/2301027/highlight/true/page/3  

and I've been through some of the same issues and problems, though they're talking about Thunderbird, not MacMail.

Please note, I'm using OSX 10.6.8 or whatever the latest Snow Leopard revision was...I have NOT switched to Lion.  My MACMAIL is 4.6, I think...the latest one.

I have done multiple things, and spent many hours, since the switch, on chats, and on the phone, and in Mac Forums, Mac Rumors, Apple Communities, asking questions and trying to make things work.  I have verified all settings, for pop and smtp, SSL, ports, passwords, ID's, etc.  several times.  They are all correct.  I've done Keychain access deletions, and Keychain Access First Aid, etc., I even had to delete my account in MacMail under "Preferences" and then recreate it. This included rebuilding my mailboxes by using Time Machine and restoring the appropriate Library files, etc.

 Also, I should note I first changed the settings to inbound/outbound.att.net as per the Help Page chart at ATT, only to realize that I was supposed to use the same old "pop" and "smtp" att.yahoo..com accounts.  I've pointed out this contradictory info to ATT Customer service guys via live chat and via phone--they list different settings on different pages.   They have been unable to help, and suggested Connecttech, but I don't feel I should have to pay someone to fix this, unless it's absolutely a last resort.

Here's where I stand right now: I am able to receive and send msgs., via MacMail with no problems at all....as long as I have previously logged in to ATT/Yahoo home page on my web browser that morning.   I've checked the "leave me logged in" box,  but even so, every morning when I open mail, I get the little "caution triangle" error msg. and  that I can't connect to the pop server, and so I have to open my browser, log out, and log back in.....voila! after doing this, MacMail will receive msgs.

I've checked the webmail, and chosen "POP my msgs."---but still, every day I have to go through this process of logging into the ATT / Yahoo home page.....sometimes, even in the same day, I may have to log out and in, for MacMail to "connect" to the pop and smtp servers.    So it's obvious my settings in MacMail are correct (??) and I can't figure out what the heck's causing this issue.

Any ideas?