Depending on your definition of "periodically" you may lose almost as much time to syncing back than the outage would have caused without the local mirrors.
I've written scripts that do this. Any request for a repo is polled against the local repo server that makes sure it has the repo, and then quickly checks to see if the repo's out of date, caching the resulting file if the repo can be reached. If the repo can't be reached, just have the proxy deliver the old fileset. So the local repo gets updated, or at least attempts to update, with every hit against it. I had some other logic in the script to only check freshness every 10-15 minutes, so that during times when a lot of machines were pulling, they were essentially guaranteed to all get the same version.
This is certainly one of the better ways to do it - when I see a word like periodically I assume it means daily/weekly/on some sort of calendar-based schedule, which isn't necessarily the case here.