Travis CI is not updating checks in PRs

The checks in pull requests seem to no longer be updating after Travis CI runs. Examples:
* https://github.com/ampproject/amp-toolbox/pull/677 (travis-ci build [669641764](https://travis-ci.org/github/ampproject/amp-toolbox/builds/669641764))
* https://github.com/ampproject/amp-toolbox/pull/676 (travis-ci build [669638448](https://travis-ci.org/github/ampproject/amp-toolbox/builds/669638448))

Possibly related to [Deprecating GitHub commit status API updates for GitHub Apps-managed repositories](https://blog.travis-ci.com/2018-09-27-deprecating-github-commit-status-api-for-github-apps-managed-repositories)?
Additional reading: https://travis-ci.community/t/github-status-not-posted-on-commits-on-repositories-using-legacy-service-integration/7798

Start by comparing the Travis CI builds linked for pull requests 677 and 676 with the checks shown on GitHub. Read the linked Travis CI and GitHub commit-status references; done means identifying the integration failure and restoring updated PR checks.

Written by the indexing model from the issue text.