Just to clarify, I'm talking about integration testing the service itself - posting a payload, saving to the database, producing messages to a mock queue, etc. Test the entire service in isolation from other services and validate that it is behaving correctly. Not end to end across services. You should be mocking out all service dependencies and testing against the contracts for those systems.

Our API tests run flawlessly every time because they write against an isolated database with well-defined endpoint and messaging contracts. They also execute all remote operations against a mock API that conforms to those contracts. This is perfectly achievable.