We could ask our developers to run the tests before every push, but sometimes people forget. Maybe they didn't forget, but it's a small change and it doesn't seem worth going through a full test run for something so minor. (Have you ever heard somebody say, "It's only a CSS change"?) Making sure that the tests are run and passed before every push to the centralized source code repository takes discipline.
What do we do if our team lacks discipline? What if we still keep getting failures that should have been easily caught, even after we have asked people to run the tests before they push the code to the central repository? If nothing else works we could have a discussion with the developers about enforcing this rule.