This looks to me like an overloaded backend service/daemon. I recently reconfigured one of my websites and tuned the PHP settings of my daemon to match the expected load of the website. If you tell the daemon to spawn too little PHP processes/threads eventually it will drop requests if too many come in at the same time, which is what leads to those pages without CSS. If it was a network traffic issue you would either just wait a long time until the TCP retransmits get through or the server would just reset the connection which would produce some error message in your browser after a short time.
I don't know whether you already have a reverse proxy/web accelerator set up yet, but that might help with this problem.
