If Siri can’t remember your relations you are likely syncing your contacts with Google Apps, Gmail or Exchange Server. This is a limitation of Microsoft Exchange Sync, a protocol that google licenses from Microsoft to support their Google Sync service.
You tell Siri to remember that your Father is John Appleseed, she acknowledges your request. Siri remembers your relations by adding their name to your contact info in a section called relations. But the Exchange Sync protocol does not support these “custom” fields so when the phone tries to sync with the server this info gets lost.
You have two options:
A: Find your Fathers contact info and write Dad in the nickname field. Some have had success with this but I haven’t gotten it to work. Also this does not solve the problem of Siri not being able to store the info for you by telling her My Father is John Appleseed. Siri will also not know that Father = Dad.
B: Set up a free iCloud account and move all of your contacts there.
C: The iPhone does not limit you to the number of address books you can sync. So set up a free iCloud account and enable address book sync. Create a new contact in the new address book and add your info. Go to Settings > Siri and assign this contact to the My Info field. Now Siri has access to an address book that she can modify with extra relations. This contact is independent of your main address book. You can continue to use Exchange Sync for your other contacts.