After using the OPEN API for some time, both in the internal page (http://hostname:8080/api/), and from an external soap client, it simply stopped working even though the internal API page is still available.
Seeing error "405 Method Not Allowed error" when attempting to run rest calls against the OPEN API that worked in the past.
This could be a cookie issue. If a user fails to login, or their account gets locked or their permissions modified in EEM, the API can hold onto a now invalid session cookie and will throw authentication related errors.
The solution is to clear the cookies from your application, either the browser for the internal API page, or the external REST Application. Once done a new login and cookie will be created and the calls should work again.