When It gets deindexed then it disappears from Google search results and comes back to search results when it reindexed. It has happened 2-3 times in past 30 days.
When it disappears from the Google search results, as keyplyr suggests, it is still in the "index". The site: operator search is not always a consistent gauge, and is subject to Google's own internal ranking cycles, and I wouldn't depend on it to provide any kind of granular indication of how the page is doing.
I would suggest that you check to see if it responds to a search for a unique text string that you know appears on the page, searched in quotes. If the text string is unique and you're not penalized, it will probably appear. Note also that by varying the your quoted text string queries to include different keywords, you can get a sense... af least corresponding to the old keyword in anchor text model... of what phrases it's best optimized for.
If the text is not unique, but belongs say to a manufacturer's description that is used by 300 other pages, even clicking on the link in Google that repeats the search to include the omitted pages may not bring your page to the surface.
Very possibly the page is an edge case, in that shadowy area between visible and what we used to call "supplemental" results. I can think of a million reasons why it might come and go, all related pretty much to linking, both external and internal, and to uniqueness of content.
If you depend on news or blog backlinks, eg, that's another variable, as they will diminish in value as they are absorbed deeper into the linking site's structure.
It's unlikely that someone's hijacking your page, but that is another possibility. If so, more than one page is likely to be affected. In the case of hijacking, when you search text strings in quotes, you might be able to spot your quoted content on another domain.
Please report back when you've given these things a try, and good luck. Edit: Fixed typo.
[edited by: Robert_Charlton at 3:07 am (utc) on Jul 13, 2018]