Though I could not resolve the issue directly but did a trick and it worked.
1- I clicked the item from Search result. Then copied it to a new folder where it appeared.
2- Deleted the item from original folder and again copied it from new to original folder and it worked fine.
Deny access right always has the highest priority. You cannot revoke it with Allow access right later.
Set Allow access right for Item Read and Descendants Read for your role:
And for extranet\everyone break the inheritance on the item:
With that set, extranet\everyone will not have Read access, cause there won't be any rule which allows it. You can use ...
By putting the X in Everyone you are effectively adding an explicit deny to literally everyone, including SecretPageRole.
Not done it but if you can just remove the green tick from Everyone it will become an implicit deny and not affect inheriting roles.