By default, your iOS device will synchronize with the last three days of email on the server. You can change this value to as much as No Limit. Please note that longer periods of synchroniation will take up more memory on your phone.
Go to Settings > Email, Calendars, Contacts
Tap on the name of the account (it may appears as your email address, 'Exchange', or UTmail). You will see the following screen:
Tap on Mail Days to Sync and choose the desired length of time.