Google Search will start de-indexing your web pages if your site has been down for more than a couple of days.

Google will start de-indexing your pages from search results if your website has more than a few days of downtime.
This is noted by Google’s Search Advocate John Mueller during the Google Search Central SEO office hours hangout recorded on December 10th.

An SEO named Aakash Singh called the livestream to ask Mueller how he can minimize the impact on search ranking while his client’s website is down for over a week.

Unfortunately, it is not possible for Singh and his clients to deactivate a website for a week without negatively affecting their SEO and search rankings.

If a website’s pages become inaccessible, it will only take a few days before they start to be deindexed, Mueller explains.

Mueller goes on to suggest an alternate method of handling planned downtime, but that still doesn’t guarantee that no harm will be done in the short term.

Google’s John Mueller On The SEO Impact Of Website Downtime

If a website is down for more than a few days, whether planned or unplanned, there is no way to prevent a negative impact on search rankings.

Mueller said :

“For an outage of maybe a day or so, using a 503 result code is a great way to tell us that we should check back. But after a couple of days we think this is a permanent result code, and we think your pages are just gone, and we will drop them from the index.”

“And when the pages come back we will crawl them again and we will try to index them again. But it’s essentially during that time we will probably drop a lot of the pages from the website from our index, and there’s a pretty good chance that it’ll come back in a similar way but it’s not always guaranteed.”

A key point to remember here is that the impact of an extended downtime will outlast the duration of the outage.
Your pages won’t come back immediately, and when they do, there will be big fluctuations in search rankings before things set in.