Are you with him when these episodes begin? What exactly is your son doing when it happens? Keep a journal of what your son eats and his activities when these things happen and maybe you'll see a pattern more than just "he's outside when it happens."
For instance, is he spinning around or rolling down hills? Is he swinging on a swing and maybe getting motion sick? Is he doing a somersault marathon?
Could he be getting stung by something? Is he rolling around in grass or leaves and getting coated in pollen? Is he drinking enough fluids? Eating enough?
Take a really close look at what he's actually DOING physically. When I get dizzy from vertigo it always makes me throw up. There are several possible causes. When I was a kid it often was from rolling down hills. Migraines cause terrible vertigo for me. Sudden allergies from inhaling a wad of pollen or dust could do it to me. Being dehydrated causes vertigo. I also have reactive hypoglycemia, so I have to keep an eye on my blood sugar. If it gets too low too fast, I get vertigo. Ditto if it goes hyper. And as I mentioned, vertigo always makes me throw up. And throwing up always makes me want to sleep.
So you'll want to find out what's causing the vertigo: if it's play, if it's migraines or an inner ear problem, if it's something else going on... keep a journal from here on out. Talk to his pediatrician about how concerned you are and what could possibly cause vertigo in a child and how you plan to keep a journal. If he still doesn't seem to take you seriously, then change pediatricians. You also should ask for a referral to a pediatric neurologist.