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Suddenly that site has disappeared from Google search and it only appears if you append the site: operator to the search query.
What could be the reason. The site has lot of content but nothing new was posted in the last couple of months.
Could that be a reason for the penalty?
I don't think you can automatically assume it's a penalty. It also could be a technical issue on either the site itself or on Google's end. Try a regular search for the domain name - example.com - and see if the domain root or home page is #1.
I wouldn't surmise it's a penalty, especially if it's a large site with a lot of IBLs. How long had it been since any content was updated, and how long since there were any fresh, decent quality inbound links.
I'd have to dig out which ones, but there are several papers out there that very specifically mention freshness as a factor that's taken into consideration. And another recent patent application as well, that goes into computing average age for the link profile.
More specifically to your question;
Can Rankings Vanish Because A Site Is Not Updated?
The answer is no, there must be other factors at play.
Links are a completely different story of course.
I am trying to figure out the reason for this. There are no violation of Google webmaster guidelines and its an extremely popular website.
Try a regular search for the domain name - example.com - and see if the domain root or home page is #1
Yes, the site is the #1 result
How long had it been since any content was updated, and how long since there were any fresh, decent quality inbound links.
Though new content was added to the site some two months ago, it continue to receive fresh inbound links daily from quality sources.
I have seen sites with very weak linkage go south, but that's more of a combo of stale and not nearly enough link love, if any at all, that's worth anything, and no new ones for years.
That wouldn't be your case, though.
Also, do you have a Webmaster Tools account? That can be a source of information from Google that you can't easily discover any other way.