If AA makes a significant change to your schedule, you will have the option to get a refund and rebook on another airline. This, of course, is only helpful if prices have not gone up.
If AA makes even a minor change in your schedule, you can rebook to flights which are more convenient to you on the same day or (usually) one day before or after. I changed my flights last year based on a less than 10 minute time change. In addition, after 9/11, months ina dvance, AA cancelled my morning flight to HI and rebooked me on the afternoon flight. I had them rebook us on the flight the night before. AA then added back the morning flight and they also moved us back to our original flight.
If AA goes out of business entirely, then trip insurance may help if you get the right insruance. Read the fine print carefully as I have seen that some policies don't cover you for this reason if you book through AA directly.
There is really no protection if AA is flying, the remaining schedule is lousy but gets you to your destination and your tickets are cheaper than any other otpion.
Best of luck -- Suzanne