You are mentioning the mysqldump, and it might be linked to the problem. If your mysqldump takes long time, and lock tables, it might cause the requests to your server when tryig to save posts, to time out.
It could also just be a plugin that is messing something up, server-side settings that have errors in them. It could be that your functions.php spits out some data when it shouldn’t, messing up the save-function. It’s hard to tell from that little information.
The list of possible causes for this problems is endless, so the only way to figure it out is to start logging.
I’d start with installing Sentry. It’s a tool that helps you find any errors, both in the frontend and backend. They have a free plan.
Then install the WordPress Sentry plugin.
Make sure you enable both backend AND frontend logging, there might be clues to what’s happening in the JS console, and Sentry will cover this.
If you are already logging errors, check your log-files (both the wordpress-error-log and the webservers error logs).
If you can recreate the error yourself, then look in the networks tab in your browsers devtools, and see what the network requests contain, and what the response is.