Error reconnecting to the database while updating/publishing more that 10 posts for a custom post type

I’m using directories pro plugin for one of my client’s site and it created a custom post type for listings. The problem that I’m facing is when I’m trying to update/publish more than 10 businesses simultaneously by opening then all in new tabs and clicking update, all of them give an error:

‘Error reconnecting to the database’
Here is the screenshot of that error: https://prnt.sc/vyyfyd

after which the CPU usage goes up for a while and then returns back to normal.
Is it not advisable to update that many posts simultaneously?

The hosting that I’m using is Godaddy VPS, 2 CPU core, 4GB RAM

The error log that I receive in cpanel error log is:

PHP Warning:  mysqli_query(): MySQL server has gone away in /home/../public_html/wp-includes/wp-db.php on line 2033
PHP Warning:  mysqli_query(): Error reading result set's header in /home/../public_html/wp-includes/wp-db.php on line 2033
PHP Warning:  Error while sending QUERY packet. PID=31687 in /home/../public_html/wp-includes/wp-db.php on line 2033

I have already increased the max_allowed_packet value to 1024M in my.cnf, still the issue is not getting resolved.

Please help what further steps should be taken to fix this?