@bshag4lv, you need to do the burn action 3 times on a pile of leaves before it goes away, that's why it seems like it "just goes out" to you.
If you wait too long between burns, you will need to do it more than 3 times because new leaves will be added that take it back to needing 3 burns.
I suggest waiting until the very last day of Autumn to bother burning, or even the very beginning of winter. Piles will just come right back anyway until Autumn is over.
Also, once you install the mod that keeps the piles from rotting, it will stop new piles from going foul, but any piles that existed in that state already stay that way I think....I recall that being what happened when I started using the mod.