At this point we are doing basic debug…
I would start by disabling all plugins (or start with your custom plugins first). Navigate the backend and see if the issue occurs.
If it’s all good, then enable each plugin 1 at a time and check the backend after each plugin is enabled.
If the issue occurs when all plugins are disabled, I would try a fresh install of WordPress.
If it still occurs with a vanilla WordPress then it’s going to be a server config issue. Check all logs, including Apache and MySQL. Ensure permissions are correct (doubtful that’s your issue as it’s sporadic but never hurts.) and ensure all Apache/PHP extensions/modules are installed that’s required for your setup.
Are you using a shared host or a dedicated server? Is it a cloud server? How is PHP running? (cgi, fastcgi, etc.) Are you using APC and/or memcached?
Use phpinfo and make sure everything is good, or at least matches your local dev.
Posting your phpinfo and httpd.conf would be helpful too. Also a list of plugins you are using.
Is this ONLY on the backend or is this happening on the frontend too?
If this is only backend, I would first assume a plugin or a corrupt WordPress install. I assume you have a (few) custom plugin(s). I would start by disabling them then going from there.
I see some encoding issues in your image. What are you setting the PHP/MySQL encoding to?