I'm having a strange issue that after a period of time, the webpage cannot find the css and JS files anymore. They all give a 404 error. This results in prices displayed in USD instead of EUR and the admin page not reachable.
The issue is resolved when I restart the apache service on my server. Not when I clear the cache.
Any idea why this happens? It started a few months ago when I started using virtualhostfiles to host different websited on one server.
From your description, it does seem like a web server issue and not related to Magento.
You will need to make sure that Apache is configured correctly (especially the virtualhostfiles) in ordet to resolve the issue.