Weird 404 error in the title of the page on the first request. After the second and subsequent response 200 OK. What to do?

Question

Google

Good afternoon, ladies and gentlemen!
About a month ago, I noticed that the pages of the site began to fall out of the Yandex and Google index due to the return of 404 codes from these pages. At first, I sinned on the jamb of robots, since the server response, when checked through the webmaster panel in Yandex, gave out 200 OK for these pages.
But the pages continue to drop out :(
I decided to run through the "View as Google-bot" and what I saw:

The page loads completely and has a normal weight, but HTTP / 1.1 404 Not Found is transmitted in the header .
How can this be? I'm on the site no serious Haven't done any rework in the last year
CMS MODx
Today's Observations
- First Request Page Responds to 404
- The second and subsequent answers go 200 OK
What could be the reason for this?
In the pictures, I emphasized the difference in the text of the answers at 200 and 404:

and

Answer 1

After much thought and not very long searches found the reason.
I wrote a little higher that I decided to try to substitute another template. In the end, there were no problems. But when installing the replacement template on the main page, I got the following:

This tells us that the main page should not have a publication date.
We go into the page settings and delete the publication date:

After that, it seems like Google returns the server response 200 OK. And Yandex both gave 200, and gives 200. Glory to Google! :-)
Sorry if I bothered anyone. I hope this observation is useful to someone.

Answer 2

I see a slightly different source code for the page in the browser. Very strange.

Answer 3

Maybe your site gave out a 500 error, and nginx perceived it as 404?
MODX Evo?

Answer 4

Once again, good afternoon. New points have emerged on this issue.
It is possible that the error generated due to the publication date and nothing to do with it. What I noticed today:

I.e. on the first call, a 404 error is thrown, but on subsequent calls, a 200 OK response is returned.
I'm downright confused. Help :(