we had issues with one of the sites, where the homepage was 5 days old, even though there were new posts every day. I was checking for possible plugin conflicts and so on.
I noticed that when the plugin is installed, the Garbage Collector event wp_cache_gc is scheduled only as a "One-off event". So I have to set the Scheduler -> Timer to 3600 seconds and hit "Change Expiration", then I can see that it's scheduled properly. Perhaps this stopped the homepage from refreshing?
The wp_cache_gc is also not scheduled when upgrading the plugin from older versions (0.9.9) or switching from "Use mod_rewrite to serve cache files." to "Use PHP to serve cache files.". So we have to hit that "Change Expiration" button again. That means each time we tweaked some setting, the issue came back.
What's most confusing is, that this is not indicated on the WP Super Cache options screen, so we were not aware of any of these issues. There is visible check of the garbage collector cron job.