reinforcement plates are a good idea
I have seen this a few times and the plates are definitly a requirment. make sure to undergaurd the plates so they don't rust, also be sure to use a pretty good sized gauge of steel so it's nice and solid.
Once welded in this should fix the issue for life.......oh and usually if one side goes your other side isn't too far behind. Insoect for cracks and if there is even a hairline I would replace both sides. It actually would be a good idea to do both sides anyway but I know it can be costly.