It seems that it's very difficult, even impossible; to have master doctors before the game is "completed"!! I never had some before that too. And it's the same when your doctors have others skills than healing, they always prefer to do something else and they never go back to studying the plants by their own (as building. I noticed that they like to make exercise and if they succeed, they get some building skills!) I have some villagers who became master doctors by their own after I completed the game and only if it's their only skills. Many of them were trained to heal sick villagers when they were kids! Take care, if you have a doctor who is a runner, he is each time the first to heal and so the other doctors fail!!

I don't know exactly how many heals it takes to have a noticeable amount of skill but it could be from5 until 10 times (each heal is a little noticeable, anyway)
Remove them after it says "This villager has improved at healing" and when their acting is "nothing".