Is it okay to keep reapplying for the same job posting that you have failed in before every time they have an opening? Or how long should I wait in between to not be obsessive?

If nothing has changed since the previous job application, then there's no additional value for the company and therefore it's unlikely for them to reconsider.

The exception is if you are sufficiently qualified for the role, but did not market yourself well. In this case, you may want to consider your value proposition to the team and why they should hire you instead of others.