You take a company down, and automated sourcing puts them back.
Block company from the company list or from Company sources. Published jobs for that employer are archived. Backfill, CSV and XML import, and API bulk writes reject them. The company stays on your board so you can unblock later. Unblocking does not republish the archived jobs.
You can still post a job for them yourself, and employers can still post if that is enabled on your board.
See Company blocklist.