Because the perseid showers result from the debris of comet swift-tuttle, which ( could be wrong) has an orbital period of 133 years, and an approximate orbit circumference of 2 billion kilometers, so it has time to throw off a lot of material, both approaching and leaving the near sun part of the orbit. It’s also 16 miles across, so it has a lot of mass it can lose, and all of the material it loses is also orbiting the sun. so it’s not like a static ring that the earth can clear out in one year.
The Leonids occur from the same process but from the comet tempel-tuttle, which has a 33 year orbit, and I believe that both comet start shedding material when the get about the same distance from the sun as the asteroid belt.
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