Julie,
I'm no physio but I do believe that wearing ankle supports (or any other support) stops you rebuilding the strength in any injured part. Perhaps the problem is that you went back to running too quickly after the last injury.
Have you had your gait / shoe type checked? Perhaps you need more support than your current shoes are giving you.
Also, are you doing any flexibility work? If your calfs are particularly tight you probably aren't absorbing the shocks from running as well as you could be.
I believe that when people get injuries in their main joints (ankles, knees etc) it has a lot to do with the stabiliser muscles not being developed. To strengthen the muscles around your ankle try some one legged squats (no weights needed) and some standing on one leg with your eyes closed. Anything that involves one legged balance really helps with the ankle muscles.
Before you heed any of what I've written, it's worth remembering that I ain't a professional and this all comes from what I've read. Physio should be your next port of call.