It takes a long time for a bungie cord to deteriorate. I've been using the same bungies for years and years, even left outside. When they begin to fray they are very inexpensive to replace.
If the wind blowing an awning is strong enough to break a bungie cord, there will be more problems than with just the cord. The entire awning material will be ripped to shreds too.
Besides, you don't want THAT much tension on the tie down. That much tension will cause undue stress on the awning arms itself and bend them or break them. You just want enough so if the wind blows or the trailer rocks, or the awning attempts to lift up, the straps keep it from flipping over the the camper and getting destroyed, or flopping up and down. Over tension can cause a lot of problems. You definitely want some spring in the tie downs, but not so much it's rendered useless or so much it damages something. That's why I've found bungies work very well.