No. There is not limit as to how many times you can renew your O-1 visa and there is no limit as to how many years you can spend in the U.S. on an O-1 visa. You can keep renewing your O-1 status/O-1 visa indefinitely, as long as you qualify.
Please read our blog post on whether you can obtain 1 or 3 years when renewing your visa when you click here.
If your goal is to stay in the U.S. permanently, you could also qualify for an EB-1A green card (you can either file a self-petition or your employer can sponsor you for the EB-1A green card), EB-2, or EB-3 green card. Applying for a green card is a great solution if you know that you want to live in the U.S. permanently. After 5 years of being a green card holder, you could also apply for a U.S. citizenship.
