I too have been plauged by bad ankles, ever since I was a teenager up until a few years ago, I badly sprained my ankle a couple times a year, this really cut into my hiking life, as it would take up to a month to fully recover.
so what changed for me?
a couple years ago I started cross country skiing, and the next summer I had markedly fewer problems with my ankles. I realized that the instability of being on skis strengthened all those small stabilizer muscles in my ankle, helping prevent further damadge. I can see how a wobble board would have the same affect.
you can do calf raises, where you stand on the edge of a stair and rock up on your toes, starting with body weight and adding weight with dumbells as you get stronger, also good to do these on one foot.
I've also noted good strengthening results from using a stairmaster machine, but standing on the balls of my feet so that my ankles and calves were targeted.
since you mentioned that this is a recurring problem, I might also suggest some massage therapy to break up old scar tissue in your ankles, allowing the muscles to align properly, thereby helping to prevent further problems.
I've also noticed the majority of my injuries occured at the end of the day, when I was hungry and thirsty. Ever since I've made a point of making sure to eat at the end of the day, rather than stopping after lunch, and I've had fewer problems
plus, the better shape you are in in general, the less likely you are to be fatigued, the more likely you are to not have problems, and the longer you go without injuring your ankles, the less likely you are to injure them in the future.