Why is it neccessary to type in (www.) before a website when on an intranet?
Unless you were just kidding, the answer is that an intranet accesses items on the corporate network with the option of accessing the internet (if it has connection to the internet) where as a strictly internet connection will usually auto-direct to the right website with out the www. It depends on how the intranet is set up for your business... at least, this is how the IIS book I have from 2 years a go dictates it.
Anyhow...
To answer the main question (why is the website sometimes down?):
The reason why it sometimes doesn't load is because either your intranet runs through a server (or 2 or 3 or 4 etc..) which process the data as it's being sent and recieved and then sends it to the specific machine you're using. If you're using terminal based systems, like the hospital I work at, then you're more likely to run into delays which result in the "cannot connect" message, or network data collisions which result in the errors you described. Network collision is a normal thing and happens on all networks, even the internet. It usually shows up on a single home users machine as lag or a webpage timeout. If you're on a large company intranet, you're likely to have more network collision with more people all trying to use the system at the same time, and not having enough servers or routers to handle all of the requests.
I hope that helped a little. I got most of this information from the IIS book, a router manual and from a website I looked at a while back but no longer have the link to.
SoooOO!...... if you're accessing from an intranet (like I do sometimes) it's more likely to timeout or not connect during higher traffic times, and you can usually just hit "<ctrl> r" to refresh the page in a few seconds... possibly requiring a few refreshes.
Alllso, it could be the site you're trying to view getting too much information to process, but that is a lot less likely. :-)