Does my Skype status ever change to 'Away' automatically?

Yes, it can, after you specify a number of minutes.

See image below: Go to the Skype Options, then to the General Settings, and then you can specify when you want Skype to change your status to away. Hope that helps!

I'm unable to comment, still, so - have to bump it.. Just felt that the answer was incomplete! :)

At their FAQ page, What is a status setting and how do I change it in Skype for Windows desktop?, it's also mentioned how to get Skype to NEVER report idle time (?) /set status:

If you have a value of 0, you will never appear as Away unless you manually set this status by clicking on your status icon and selecting it from the list.

P.S. Got here via Google query, "skype block idle time".