This issue can be resolved with the following steps:
- Download and install the latest version of iTunes. You can also check for updates in iTunes by choosing Help > Check for Updates or by using Apple Software Update.
- Open iTunes.
- Choose Edit > Preferences.
- Select the Devices tab.
- Click the "Reset Sync History" button and then click OK.
- Sync the iPhone or iPod.
- During the sync, you will be presented with a list of conflicts between contacts. Select the contact with the correct birthday for each conflict.
- After selecting all of the correct contacts, select the option to Sync the changes.
Once the changes have been synced, the birthdays should appear correctly on both the device and in Outlook.