Who maintains the web server for you? If there are no error logs in Expression Engine, I would start checking the web server logs and PHP logs. It seems like some session time out issue, which can or could be caused by a misconfiguration in your server settings.
What settings do you have as a session in your EE settings? Try changing that setting and see if it works.
Settings > Security & Privacy > Settings
Check the Session Type. If you have some browser setting that is erasing or blocking cookies, and you have the cookies option set, that might also potentially cause issues. Try testing a different browser as well, just in case.
Try disabling EE Add-ons. If you are sure this is not an issue with your browser and EE sessions, then its almost very likely a misconfiguration in how PHP is storing sessions in your server.