Database containing Birthdays is generated by iOS itself, managed by Apple.
We are only able to display contents of this database.
If age is missing it's not in your database somehow.
To force iOS to rebuild this database:
- Go to device Settings
- Select Contacts (or Mail, Contacts, Calendars in iOS9 and below)
- In the Accounts section select the one containing your Contacts (in most cases iCloud one)
- Turn OFF Contacts
- Reboot your device
- Turn ON Contacts again