Permalinks Break Upon WP Updates

We have many sites that all seem to have problems with 404 errors on various pages after WP version updates. The fix is to re-save the permalinks after updates, but I’m wondering, is there some way to automatically save permalink settings either after updates, or even better, every 24 hours? Going into 20+ sites to save permalinks after every WP update is cumbersome, and time-consuming.