Oltre ad Apache entrano in gioco altri fattori. Che linguaggio usa il portale, php? Quale? 5.6, 7.0, 7.1....
Come è configurato il portale, a livello di apache? cgi, fast-cgi, suexec, fpm ecc ecc.
Che backend di database usi? MySql, mssql, oracle, mariadb....
Comunque, a occhio sembra un collo di bottiglia da qualche parte relativo al numero di connessioni che, quando vengono superate, inchioda tutto.
Verifica per esempio se hai qualcosa di questo genere nel caso di php e virtual hosts
codice:
<IfModule mod_fcgid.c>
                                FcgidIdleTimeout 300
                                FcgidProcessLifeTime 3600
                                # FcgidMaxProcesses 1000
                                FcgidMaxRequestsPerProcess 5000
                                FcgidMinProcessesPerClass 0
                                FcgidMaxProcessesPerClass 10
                                FcgidConnectTimeout 3
                                FcgidIOTimeout 600
                                FcgidBusyTimeout 3600
                                FcgidMaxRequestLen 1073741824
</IfModule>
<Directory /var/www/clients/client1/web11/web>
                                <FilesMatch "\.php[345]?$">
                                        SetHandler fcgid-script
                                </FilesMatch>
                                FCGIWrapper /var/www/php-fcgi-scripts/web11/.php-fcgi-starter .php
                                FCGIWrapper /var/www/php-fcgi-scripts/web11/.php-fcgi-starter .php3
                                FCGIWrapper /var/www/php-fcgi-scripts/web11/.php-fcgi-starter .php4
                                FCGIWrapper /var/www/php-fcgi-scripts/web11/.php-fcgi-starter .php5
                                Options +ExecCGI
.....
</Directory>
e che dentro a /var/www/php-fcgi-scripts/web11/.php-fcgi-starter ci sia qualcosa di questo tipo
codice:
#!/bin/sh
PHPRC="/etc/php/7.4/cgi/"
export PHPRC
PHP_DOCUMENT_ROOT="/var/www/clients/client1/web11"
export PHP_DOCUMENT_ROOT
# The variable PHP_FCGI_CHILDREN is onyl useful for lighty or nginx as apache
# mod_fcgi will control the number of childs themself and never use the additional processes.
# PHP_FCGI_CHILDREN=8
# export PHP_FCGI_CHILDREN
PHP_FCGI_MAX_REQUESTS=5000
export PHP_FCGI_MAX_REQUESTS
export TMP=/var/www/clients/client1/web11/tmp
export TMPDIR=/var/www/clients/client1/web11/tmp
export TEMP=/var/www/clients/client1/web11/tmp
exec /usr/bin/php-cgi \
 -d open_basedir="/var/www/clients/client1/web11/web:/var/www/clients/client1/web11/private:/var/www/clients/client1/web11/tmp:/var/www/sito.com/web:/srv/www/sito.com/web:/usr/share/php:/tmp:/usr/share/phpmyadmin:/etc/phpmyadmin:/var/lib/phpmyadmin:/dev/random:/dev/urandom" \
-d upload_tmp_dir=/var/www/clients/client1/web11/tmp \
-d session.save_path=/var/www/clients/client1/web11/tmp \
-d sendmail_path="/usr/sbin/sendmail -t -i -f webmaster@sito.com" \
 $1

Oltre al log di apache verifica i log del database, potrebbe essere un problema lì...