This problem has be stumped beyond belief. I have a website, hosted on CentOS, served from Apache. It has an SSL certificate installed, but the behavior exists for the SSL as well as the non-SSL side (i cleared out my .htaccess file to make sure it wasn't causing the issue).
When someone tries to access the site from outside our network (where we host our own DNS servers), they get a connection timed out error. If I upload a file (changed or not) to the site, it will become visible to the outside for a short period of time, about 5 minutes or so. I can see the site fine from inside our own network at any time, and using our own DNS servers. I can also see it from our own network using Google's DNS servers (18.104.22.168 and 22.214.171.124). The access_log and error_log files don't show the requests that fail, only the requests that are successful.
I have no idea what could be causing this, or where else to look for clues. I know I haven't given much information (configs, etc), but I don't know what information would be relevant. Any ideas? I'm hesitant to link to the site as it is an unlaunched client's site, but if it is necessary, I can either PM it or post it.
UPDATE: I also realized that when the site is timing out, I can't ping the server IP.