texasfire's suggestion fixed it for me, changing the TLS cert from none to com.apple....
The problem i was experiencing:
smtpout.secureserver.net was working fine with same and other user accounts on different devices, a win7 pc, iphone 6 and a blackberry classic but on a mbp it was saying offline and that it couldnt connect to the server. Even had the same result with the connection doctor that the OP had. Pretty sure this problem started after mbp owner upgraded to El Capitan the other day, but was brought to my attention today. They had no problems before upgrading.
After changing the TLS cert and setting to a non-ssl port (25) mails started sending no probs. Shut down the system and opened it back up and tried to send and got the error again. Went into the settings and the TLS was set to none again. Set it back, closed the mail app, opened it, check, its still set this time. Shut down system, opened Mail back up and it is set to TLS still, test emails sent successfully. Problem solved, i hope. MBP owner does not have the gumption to go through those steps every time OSX decides to revert back to no TLS for what ever reason.
So there appears to be a couple of problems with El Capitans mail app, one of them appears to be that it doesnt remember stuff when you select it or is for some reason going back to a default i cant change, and it is clearly effin up peoples smtp settings. i read about people experiencing the same exact thing with gmail and icloud email after upgrading to el capitan, so i do not think go daddy is at fault here. Maybe there is some setting on their end thats causing this but im putting the blame on apple.
Thanks texasfire. All the steps i went through, changing the TLS is one i wouldnt have guessed as im not exactly sure what it even is.