Email sync between iPhone and iMac

Of course check each device to ensure the settings are correct. Assuming you have and the problem persists then it's time to contact AppleCare then, please use the AppleCare Contact Info link to find the number in your area.

You don't mention how you are syncing them, I recommend you use iCloud if you are and are having an issue then a) please consider beginning to use iCloud and b) if you have an issue, please give AppleCare a call and they can help coach you.