Hi Suketu,
As the other APIs in the same extension are working fine, I would first check the affected API's metadata/registration rather than Postman or authentication.
When you get the 404, try checking the API $metadata and see if the EntitySetName for this API is actually there. If its missing, then BC is not exposing the endpoint at that time.
I would also check if there is any API path conflict with another extension. Make sure the combination of APIPublisher, APIGroup, APIVersion and EntitySetName is not being used somewhere else.
If you have Application Insights, also have a look for RT0048 (conflicting API path) and RT0037 (invalid API page).
One test I would do is after publishing the extension, check the metadata when the API is working and then again when you get the 404. If the EntitySet disappears from the metadata, that gives you a pretty good clue that the issue is with the API registration and not the request itself.
If there are no conflicts and the API still randomly starts/stops working after publishing, I would raise this with Microsoft, specially if you can reproduce it in a clean sandbox.
I wouldn't change the API names as a workaround yet, unless you actually find a conflict.
Thanks,
Sanket
