From AA Conditions of Carriage:

Tickets are valid for travel only when used in accordance with all terms and conditions of sale. Terms and conditions of sale include but are not limited to:

The passenger's itinerary, as stated on the ticket or in the passenger's reservation record,

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Due to the storm, it would have been prudent to call AA and let them know of your plans. Perhaps they would have made the changes at no cost.

In general, if you miss any segment of an itinerary, the rest of the itinerary cancels automatically - this is true on all airlines, not just AA.