Accessing eMail through Safari

My email is interfaced through Apple Mail and Safari to ATT. It keeps interrupting and becomes inaccessible from Apple Mail. I change the password and it works temporarily and works on my iPhone and iPad. Then it ceases on my desck top. I try to access the ATT account directly through Safari and it will not accept my Username or Password. I can access my mail on my iPhone and iPad. I have the latest software updates. I can open Firefox and log in and read my mail, but not through Safari. ATT cannot solve this. I have posted these issues on Apple Support before and no one responds, though some indicate they have a similar problem. I guess people with Apple do not read or care to help unless we buy into their maintenance charges.