So what is happening is that as quanity of links or competition is increasing on that keyword. So, it's becoming harder to be considered an authority and have the sitelinks displayed on that search term.
I have another domain that is in the same niche, and the site is pretty much dead. But, it still shows 6 sitelinks on a search for the domain name. So, this show me that it more about the increased competion than about my site itself.
Btw, you are correct that it will take more quality backlinks to bring the sitelinks back. However, the types of links that you have listed are better for referral traffic than to provide 'link juice'.
Sitelinks are automatically generated for sites that are the most relevant result for the keyword. So, in order to get the sitelinks you need more backlinks than the competition for that specific keyword. That's way you manly see the sitelinks on a websites url or on a company name.