Often if you leave your Skype browser open for a long time, you’ll find that your status is actually still set as “online”, rather than away – even through you’re not at your computer.
You can remedy this and make sure you’re not inadvertently showing people the wrong message.
Open Skype, and then head to “tools” up the top of the screen, and then “options”.
There, you’ll see a box that says “show me a away when I’ve been inactive for X minutes”. All you need to do is set a minute amount, and you’re good to go.