I have four email accounts set up on my new 5S. Two of the accounts will not update over home wifi, they are icloud and my verizon.net account. The two other accounts both "exchange accounts" will update instantly.
icloud and verizon will only update if I turn wifi off. Have tried both fetch and push. No effect.
Are you still having difficulty with those two email addresses updating from wifi? If so, please send us a private message by clicking here so we can look into this.
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In the meantime, please let me know if you have any other questions or concerns!