Signing in to Cox Mail on a Mac El Capitan

I have an IMAP Cox email acct. Just lately when signing in the Cox mail on Firefox or Safari, Cox does not recognize the password, yet Apple mail seems to work fine when accessing mail although there remains the problem I understand with Apple OS-X and Cox servers. If I try an access too many times on FF, my mail acct is locked. I spent  3 hrs with Cox trying to TS the problem including 3 PW changes, deleting histories, cookies et al but the problem persists. Any thoughts out there on this?