I've experienced the timeout error when SQL Server is down or I VPN from home using a different domain. Some containers fail from being unable to obtain a lock.

Try using the full domain server name in the SSIS Server table

Verify the login being used by SSIS has the needed permission. You can start a profile on the remote servers to see what login is being used on both successful and unsuccessful connections.

Review the error log for the SQL Server having connection failures. Make sure the capture Login Failure setting is enabled on the server.