Can I travel out of Thailand multiple times on a Non-Immigrant O-A visa?

As you have a non-OA visa, you have also the obligation to have a health insurance.

Yes, you will get a stamp of stay for 12 months (maximum) when your visa is still valid and maximum the end of your health insurance validity. Often the health insurance gives the maximum stay, as the new certificate you get normally 1 months before your new insurance is starting.

As James says, and each time you enter you will be stamped in for 12 months, so do a border bounce in the last few days before expiry to ensure you get a further 12 months stay

During the FIRST YEAR FROM ITS DATE OF ISSUE... YES... you can leave Thailand and reenter Thailand as many times as you wish. It's a multiple entry visa during the FIRST YEAR.

BUT, starting with the second year, you will need to have a Reentry permit to enter Thailand and keep the OA visa valid.

Re-entry permit cost is 1000 Thai baht for a single reentry, and 3,800 Thai baht for a multiple reentry permit. Available at your local Thai Immigration office or at the international airport before departure time.