I'm assuming all three accounts are G-mail accounts although it should not make a difference. Compare the mail settings from a working G-mail account, on your phone, to the one giving you trouble to see if a setting is different maybe. Is there any difference between the account name or password, as set-up on G-mail and the one in the phone. One letter or special character different, an underscore or space missing or extra, ? My iPhone 5 has one G-mail, one Yahoo, three addresses from my home ISP and two from work. After a couple minor glitches when setting them up I have had no problems, the phone should be able to handle multiple addresses easily.