What are the sites running? A content management system like WordPress? You may need to put some FastCGI tuning in your relevant php-fpm user.conf file, or in the vhost conf -- increasing various timeout settings.
Per-user tuning available under that version of php-fpm: 
/opt/alt/php-fpm83/usr/etc/php-fpm.d/users/username.conf
pm = ondemand
pm.max_children = 4
pm.max_requests = 4000
pm.process_idle_timeout = 15s
;listen.backlog = -1
;request_terminate_timeout = 0s
rlimit_files = 131072
rlimit_core = unlimited
catch_workers_output = yesAdditionally/alternately, you could tune the particular vhost conf to include various FastCGI parameters that could help mitigate your issue. Here is what I have on a demanding Drupal site under Nginx (especially the buffers):
        fastcgi_pass unix:/opt/alt/php-fpm82/usr/var/sockets/username.sock;
        fastcgi_split_path_info ^(.+?\.php)(|/.*)$;
        try_files $fastcgi_script_name =404;
        fastcgi_index    update.php;
        include              fastcgi_params;
        fastcgi_buffers 16 16k;
        fastcgi_buffer_size 32k;
        # Block httpoxy attacks. See https://httpoxy.org/.
        fastcgi_param HTTP_PROXY "";
        fastcgi_param SCRIPT_FILENAME $document_root$fastcgi_script_name;
        fastcgi_param PATH_INFO $fastcgi_path_info;
        fastcgi_param QUERY_STRING $query_string;
        fastcgi_intercept_errors on;