There is no major difference between paid and award tickets during IROPS. With significant delays or cancellations, AA should make every reasonable effort to get you to your final destination on AA/partner flights as soon as possible. Besides the option of just waiting out a delay, you can switch for free to a different connecting point, or to a reasonable alternate destination airport, or to a nonstop, whatever has an available seat (award availability is not an issue at this point). You can independently search your options, and if the app is not offering what you want, ask an agent.

All that is to say, if you want to reach your destination, look for options that keep you moving forward, and don't give up until you have to. AA will not charge you for IROPS rebooking. If you have direct costs from the delay or cancellation (hotel/meals), AA will cover these only if the issue is under its control (mechanical/crew as opposed to weather/ATC).

I emphasize these points because your go-to response seems to be to cancel your trip, but there are usually still ways to get there. If you truly have no good options and your arrival will be delayed so much that you no longer want to go, then you should request a trip in vain cancellation. This will get you a refund (note, even without IROPS or trip in vain, you can also get a refund of an award ticket anytime before departure for any reason). If you are already traveling and the issue occurs at a connecting point, then for trip in vain, AA will return you to your point of origin.