Running job in endless loop
Assuming that:
- You have the looping and sleep code in the CLR code
- You know how to call said code from SQL agent (a stored procedure wrapper if nothing else)
- Your process is ok with the occasional sub-minute downtime 
- Your process will not lose any data if it fails part way through (i.e. the next run will process the data the failed run was trying to process)

then I would propose a SQL agent job that is sceduled for every minute, and the job step itself have say, 10 retries set (advanced page) so that it will usually restart itself immediately if it fails.
Why just 10? Because if it starts consistently failing, you will want to get notification quickly (via agent job failure notification settings). That will be an email a minute.
Of course, if it fails 10 times sporadically, you'll get a false alarm notification, but you can quickly see from the job history whether it's failing consistently or just sporadically.