Does not refresh after page edits

I’m using the latest versions of WordPress and this plugin.

I’ve to manually delete the cache – too many times. Once in a while it seems to recognize the page edits, but most of the times, it keeps serving the old page.

I turned on debug, and it shows:

22:40:00 /wp-admin/post.php Post change: deleting cache files in /home2/.../public_html/mpopette/wp-content/cache/supercache/www...com/
22:40:00 /wp-admin/post.php wp_cache_post_change: Already processed post 32.
22:40:00 /wp-admin/post.php wp_cache_post_edit: draft post, not deleting any cache files.
22:40:00 /wp-admin/post.php wp_cache_post_edit: Already processed post 32.
22:40:00 /wp-admin/post.php wp_cache_post_edit: Already processed post 32.

That seems wrong – I had just edited that page and added a line. I tried other edits, clicked on Update button on the Edit Page.
The log above does says “deleting cache” but then it says not deleting. Which is confusing… and looks like the first line is a lie, and the second one is correct.

Page still shows:

<!-- Cached page generated by WP-Super-Cache on 2013-12-02 17:14:53 -->

which is nearly 20 minutes old document.

Any way to fix this?

Update: I tried again after a few minutes, andthen a new page showed up!

<!-- Cached page generated by WP-Super-Cache on 2013-12-02 17:49:56 -->

Debug log shows:

22:47:33 /wp-cron.php?doing_wp_cron=1386024452.5844719409942626953125 Cache garbage collection.
22:47:33 /wp-cron.php?doing_wp_cron=1386024452.5844719409942626953125 Cleaning expired cache files in /home2/.../public_html/mpopette/wp-content/cache/blogs/blog/
22:47:33 /wp-cron.php?doing_wp_cron=1386024452.5844719409942626953125 Doing GC on supercache dir: /home2/.../public_html/mpopette/wp-content/cache/supercache
22:47:33 /wp-cron.php?doing_wp_cron=1386024452.5844719409942626953125 prune_super_cache: deleted /home2/.../public_html/mpopette/wp-content/cache/supercache/www.....com/animation-enfants/index.html

So it eventually does fix itself, but it makes it impossible to edit the site and test it immediately.

http://wordpress.org/plugins/wp-super-cache/