They can continue learning until they die. I think most villagers who become Elders don't reach it until they are 50 unless an event gives them extra skill or they are a runner. You don't say what level medicine you've got, but it might be wise to make sure you get at least L2 or your villager will become elderly, which will mean that she takes much longer over the tasks and therefore learns slower.
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To err is human; to arr is pirate.