I have developed the online store on magento platform. Everything works fine except the Catalog price rule for sale. I have created the simple rule that applies 15% discount
As stated above by @Alexei-Zerofezev the problem is with the indexer.
I had this problem as well, the issue exists when there is an offset of the local timezone greater than +01:00.
Basically just because magento is using the gmtTimestamp for the rule date which in the above stated case results in the day before today.
Therefor I developed a small module https://github.com/Chuvisco88/Chuvisco_CatalogRuleFix to fix the issue. If someone ever has this problem, please give it a try.