Every berry type has a "grow time", which is the time it takes a berry plant to reach a new stage. This time mostly lies between 3 and 5 hours and one berry tree has 5 stages (starts at stage 1 and needs to grow a stage 4 times to become "harvestable"). For example, a Oran Berry tree needs 3 hours to grow to another stage, 4 stages => it needs 12 hours to grow. But a fully grown berry tree only stays in that stage for the normal grow time. So after 3 hours, the Oran Berry tree will go back to stage one. This is because the tree "dies" and drops the berries which plant into the loamy soil again.
I changed one thing in the 0.40 update: If you start a new save, the pre generated berries all over the region stay in their 5th stage forever so you can always harvest them.
Edit: Woops, looks like I confused this thread with your other thread about the berry time question.
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http://pokemon3d.net/forum/threads/5909/)
I think you should maintain the berry growth yourself. A type of berry can't extinct by you using all of them because you can get all types of berries from the Safari Zone Gate.