I have a question. How long catalog price rule are applied?
1. Add a new catalog price rule.
2. Wait some minutes while rule is applied.
3. Then Update this rule and click 'Save and apply' button.
4. But on store front nothing update.
I was waiting for 10 minutes, nothing update, clean cache and nothing update.
Then I deleted this rule, cleaned cache, was waiting some minutes, opened storefront and saw that my rule from second step was applied but I deleted it.
Can you tell me, why it's working?
Maybe you have in index management (System-> Index Management) set update by schedule for Catalog Price rules? This may be the reason why the changes are applied and visible after definite period of time.
Magento requires complete reindex of catalog for the rule to become active/disabled.
Here are also a few more points you can check when your catalog price rule does not apply -