Basic Troubleshooting Tips
Here are some basic troubleshooting tips that may help you solve iPhone email problems.
Check your Connection
Check the signal indicator at the top of the screen, if there are no bars or a 'No Service' indicator try waiting 10 minutes or move to another location until the service returns and the 'E' is visible next to your signal bars. If you're connecting with Wi-Fi, check the service and if unable to connect turn off the Wi-Fi by tapping Settings > Wi-Fi and use your operator network data connection.
It is also important to check your iPhone is not in Airplane mode by tapping Settings > Airplane Mode should be 'off'.
Set up Mail via iPhone
Many users have experienced problems having synced their email via iTunes, this is because email settings may vary between the media used to access them, i.e. laptop, desktop, mobile phone. If you have synced your email this way and are experiencing problems try deleting the affected email account by tapping Settings > Mail, Contacts, Calendars > Tap affected account > Delete. Now set up from beginning.
Multi Device Lock Out
Whilst this isn't a common problem, Apple recommend that if you tend to access your email from different devices you may actually 'lock out' your email which stops your new mail coming through to your iPhone. The solution for this is to increase the interval your mail is refreshed. To change this you tap Settings > Mail, Contacts, Calendar > Fetch New Data.
Check SMPT Server Settings
For outgoing mail your iPhone will use a primary server but sometimes this can be unsuccessful which is why you will need to check your other SMTP server is enabled. To check this just go to Settings > Mail, Contacts, Calender > (your affected email address) > SMPT > Check 'Other Server' is 'On'.
To restart your iPhone just press and hold the top right sleep button until the red slider appears, slide your finger across and wait for five minutes. To switch back on press and hold the sleep button again and once you have a strong coverage signal try mail again.