First off, yes a dog can die from worm infestation but it's usually due to starvation & dehydration as the intestinal worms & parasites rob his body from absorbing any nutritional content. Second, it's very possible your dog is reinfesting himself if you are not super duper vigilant in picking up every single stool at the time it is "deposited". If your not doing this regularly & this pup is playing in the yard, he can reinfest himself just by licking his paws after romping in the yard as it's fecal to oral transmission. And depending on the load, it can take up to 2 weeks to completely rid a dog's system of intestinal worms and/or parasites.