The pages may still be indexed, but the pages are ranked no where near as they used to be. That's the reason why usually the traffic falls of and possibly due to one of the Penguin or Panda updates.

Alexa may not be accurate. I wouldn't look at it for any conclusions. Do you have any real statistics from the site itself?

Alexa is just a guess, nothing more.

You need to look in your analytics and determine where your traffic was coming from .. and which traffic sources have stopped.

This type of thing is usually due to a penalty from Google, which could be in the form of an algorithmic penalty or a manual penalty.

You can check for a manual penalty in webmaster tools.

Use Ahrefs.com or MajesticSEO.com to look at your anchor text, or even look in Google's Web Master Tools - if you have over optimized anchor text then chances are this is down to Google's penguin update.

That's assuming that it's organic search traffic that you have lost.

You are spot on adamjcd. More questions need to be asked and typically you could locate or narrow down the cause through analytics.

What kind of site are you talking about? can you tell us what it is?

its not a site that attracts huge numbers of affiliates driving traffic to it, is it?

If its not your site, what's your concern? I'm just trying to understand why your interested in a site not owned by you dropping off in traffic.