why do some web pages time out while others stay up and running all day long?

Once a web page is loaded it can't time out any more.

A time out is when a request for data hasn't been replied in 30 seconds: This means the server is lagging like crazy, or under some sort of DoS attack.

A video however, consists of a large number of packets, and takes a long time to transfer. If one of the packets times out, the browser will attempt to get it again. If the video is set up to stop people using direct links, it can be denied access for the next attempt at acquiring a package, and the video will stop loading.

Most of the timeout settings are set by the web configuration, in some rare cases lowering your security can help exceed those timeouts. For movies and such when it comes to refreshing is usually because the stream drops the connection momentarily.

Every website has a server (usually more than one) that processes all requests for viewing the webpages on a website. If the server is temporarily down, loaded with many requests, etc., you may encounter problems. Every website's server is different, so that's why it happens to certain websites at certain times.

It is configured in the server, you can't change it yourself.