Has anybody had problems with AA refusing to reimburse for lost or missing items from luggage?

I travel Boston to Costa Rica with a connection in Miami several times a year. I have had numerous problems with late arriving luggage ,up to a 1 - 5 day delay in some cases. For late arriving I have never requested any type of reimbursement nor have I complained.

On a trip 2 years ago AA lost my suitcase, It was never recovered. I filed forms for reimbursements but got next to nothing because I do not keep receipts.

This past September my wife paid an overweight fee ($200) for a suitcase full of presents for friends and family. Suitcase was lost but eventually showed up 3 weeks later at my door. It was no longer overweight with many missing presents. This time we had receipts but got a letter from AA saying in part:

"In our evaluation of this claim, it has been noted that there have been multiple instances of reported baggage problems with American. Some of these claims may have been reported by members of your family or others in the same household.................we must respectfully decline this current claim."

Any advice on what I should do next?