google sitelinks not showing

Question

I am trying to display google sitelinks searchbox on one of publication houses website. The site generates lot of content almost everyday. I added the script inside head tag, which is:

<script type="application/ld+json">
     {
     "@context": "http://schema.org",
     "@type": "WebSite",
     "url": "http://www.example-site-of-mine.com/",
     "potentialAction": {
       "@type": "SearchAction",
       "target": "http://www.example-site-of-mine.com/archive/?q={search_term_string}",
       "query-input": "required name=search_term_string"
       }
     }
 </script>

NOTE: I deliberately have put example-site-of-mine as domain name.

So, its a week not since its implemented and its still not visible. I noted one more interesting thing, one of our other publication site, displays sitelinks just by searching for the publication name in google, and they have not implemented any sitelinks script at all.

What could be the reason of this behaviour? Both the sites are properly structured and follows SEO conventions resonably well, but may vary in terms of traffic, the other site which do not have sitelinks script has a bit more traffic then the one which has implemented sitelinks script. Could this be a reason as well?