This will depend on at least four things: the rewards program, how close it is to your flight date, the insurance you've bought, and to a certain extent the reason for your change.
For example, most programs won't let you cancel the flight within a certain number of days (22 is popular) and instead will only let you change it. Before that point, you get your miles back and the insurance will presumably cover the fee, which will probably be around $100. After that point, you can change to go somewhere else a lot later and ask the insurance to cover the fee. This won't work if you aren't likely to be able to fly within the next year, say as a result of a disastrous health problem, but would be workable for a family emergency that requires you to cancel your vacation.
The AAdvantage FAQ says:
Q: How do I change my award travel reservation? A: Changing award
reservations online is not an available feature at this time. Please
contact AAdvantage Reservations at 1-800-882-8880 to make any changes
to an award travel reservation. Any changes made to your reservation
after ticketing may result in a charge.
Q: How long is my ticket
valid? A: All travel on an award ticket must be completed within one
year from the date of issue.
Q: What do I do if I claim an award
and am not able to use it? A: Once ticketed, you will have one year
from the date of ticketing to fly, unless otherwise stated. AAdvantage
mileage will be reinstated for unused and unexpired award tickets upon
return of the ticket and payment of a processing charge.
If changing isn't an option, the insurance won't be much help. But if changing is an option, perhaps insurance isn't even necessary for you.