Searching is not working for new added products, though it's working for old products.
I found where the issue was. As I am using a 3-rd party extension (Sphinx search by Mirasvit) the configuration was not properly set. Previous employer made really difficult configuration where search engine was set to be hosted on a external server, not maintained by anyone. Changing it to build in search engine solve the issue.
You need to confirm following points with your new products according to Store View,
Status = Enabled
Visibility = Catalog, Search
Stock Availability = In Stock
Qty = Greater than 0
Categories = Category associated
And also make sure same setting applied for Website and Store view you can check through the Choose Store View option.
Hope it will help