When is a good time to reset permalinks?

If you are changing permalinks then you need to have a plan for redirecting old urls to new or else you will create many SEO and visitor issues. If you are redirecting immediately after you make changes then time of change is not so important. If there will be a delay in the redirects being made and tested then look at your search traffic and pick a day/time where you expect to have the least visitors on your site based on past activity.