Cron-based search re-indexing does not work

• I'm running 4.7beta4. linux.
• cron.php has permissions 755
• The watchdog reports success every hour ("Cron run completed")
• Search settings are defaults, and report "100% of the site has been indexed," which is perhaps part of the problem, i.e., that the search module thinks it has no work to do.
• Terms from new stories and pages that are added do not get indexed until the "Re-index site" button is pressed in search settings.
• Terms are found after manual re-indexing that weren't found by manual or automatic cron runs.

While I don't have access to the Apache error log directly, cpanel gives me access to what I think is the Apache log filtered for my site's events. No errors show up there.

I don't know what the algorithm is that the search logic uses to determine the percentage of the site that is indexed, but it is faulty, since it always shows 100%, even after new nodes are added.