TL;DR: Does anyone know why forcing https would break CiviCRM's cron jobs?

A few days ago, I edited my .htaccess file to rewrite URLs to always use https, using the following code:

RewriteEngine On 
RewriteCond %{HTTP_HOST} ^example\.com [NC]
RewriteCond %{SERVER_PORT} 80 
RewriteRule ^(.*)$ https://www.example.com/$1 [R,L]

That change stopped CiviCRM from running its scheduled jobs (nothing being logged, emails not triggering, etc.). Running them manually still works.

The day this problem came to light, I changed the corresponding cron job URL to https instead of http. No change.

Subdomains with separate databases that don't force https are unaffected. "Force secure URLs" was on without incident before this problem started so I don't think that's a factor.

I'm running CivCRM 4.7.14 on Drupal 7.53.