• Can I get a refund for a fare that has repriced to a lower amount?

This is called a "fare rollover". You may qualify for a refund of the difference between the fare you paid and the new, lower fare, if it is for the same fare class, minus any change fee associated with your fare. Your fare's detailed fare rules (which can be seen prior to purchase) can also be found if you enter the ticket number (starts with "001") at AA's refunds site (you can also find your ticket number if you have purchased the ticket within 13 months). There are significant restrictions, which should be read at the link below.

AA.com: Rollovers - Rules For Rollover To Lower Fare
AA.com: www.refunds.aa.com
FT: AA Get A Refund After An Airfare Price drop (fare rollover)