Promotions are not available in CD server after approved in CMS on the same day.

I created a Promotion with public Coupon for a product and approved it. I'm able to use promotion immediately  and it gets applied on the Cartline while using CMS website. When I tried to do the same on CD website, I'm able to add the Coupon and it says its been added for the first time but doesnt show it on the cartline like it does in CMS site. tried adding it again and it shows error. 

When again I go to same basket next day It appears automatically.

Can it be caching or indexing?

Has anybody experienced this behaviour? Any help will be appreciated.