How to clear an Error 15404 after a DB restart (besides rebooting)
Not a solution, but you can work around the issue by making the job owner a SQL account.

Each time a job is started, SQL Server verifies the identity of the job owner and checks that it has permission to execute the job. If the owner is a Windows account, the engine needs to query Active Directory. If for any reason that fails, the job will not run. It could be because the AD server is busy, down or cut off from the network, or that the SQL Server service account doesn't have rights.

Since it works immediately after rebooting, that makes me think it might have something to do with cached credentials. Windows will save the credentials it looks up for later use. That cache is cleared on reboot. Perhaps something is corrupting the cache.