Thats exactly what the coopers we put on my wifes F150 did...repeatedly. Got them at discount tire so rebalancing is no charge but after every 3 to 4k of driving the balance is off. Won't be buying them again YMMV
I've found if you take the truck to a different Discount and tell them the issue they'll make sure it's perfect. I guess there's bragging rights among he stores.
Jim