You can reapply for an American Express business card 12 months after cancelling the identical card. To churn at a rate approaching once per year you would need to cancel very soon after receiving each bonus.
I always keep my AMEX bus cards open about 9 - 11 months, I guess I always figured cancelling any sooner might cause issues down the road.
Of course before the new rules I was rotating business and personal cards for Delta and SPG so it was like a yearly bonus