Seeing a podiatrist would be a good idea. Also, there is a simple method I have used to strengthen ankles:
Find an sloping, paved area - a driveway can work if it is fairly steep, but a larger area is better is you can find it - and walk in circles on it. Alternating clockwise with counterclockwise is a good idea. You'll be walking part of the time on a slope that is downhill to the left, part straight uphill, part straight downhill, and part sloping to your right, so that the muscles get worked in all orientations. It's boring, but it works.
But be aware that this won't help if the issue is something other than simple weakness, which is why the podiatrist visit is a good idea. And I suggest finding a podiatrist who specializes in runners and athletes, if you can.