This is a problem I am facing in both a 32-bit install of Debian Wheezy and on my amd64 laptop with two monitors. Wheezy too.
Closed programs still show in Akonadi tray, upon right-click I do get the context menu, but it is unresponsive.
I recently closed X, to do a dist-upgrade, and smxi reported that X was still running.
This is certainly a bug, that started to show up in recent upgrades.
Have other KDE users reported anything similar?

I assume you talk about the SysTray, there are no programs in the Akonadi Tray. Also could you please specify which applications you are talking about?

Yes, it is the SysTray, all applications hang in there: iceweasel, Synaptic Package Manager, etc.

All those applications are not KDE related, so not much we can do about that. Moving this discussion to Workspace, as it has nothing to do with Graphics & Multimedia.

These applications have likely minimised themselves. Just right click on their tray icons and select the applicable quit/exit option.

bcooksley wrote:These applications have likely minimised themselves. Just right click on their tray icons and select the applicable quit/exit option.

Sorry, but not so.
Right-click will not close the unresponsive app.
It might not be a KDE issue, but something that I would have to bring to the attention of the Debian-KDE group.
I just wanted to know if other KDE users were running into same issues.

Can you please provide a screenshot of this to confirm it is the System Tray?
It could also be the Task Manager, in which case opening another application will likely cause the lingering application to disappear, unless they have been pinned there.

@bcooksley,
Difficult to take a screenshot because this is random behaviour, however I will comply with your request ASAP.
Meanwhile, I think it is the Task Manager, because opening another app. causes the lingering one to disappear, as you pointed out.

Very difficult to take snapshot because when I launch snapshot program lingering app disappears.
So it must be the Task Manager that is exhibiting this unusual behaviour.
Also, when hovering over the app, I get preview with an X and a progress bar, but not a preview of the program, because it is closed.
Context menu launches but does not work.

Ok, this is a known Task Manager bug then. Simply opening another application, or closing one will cause this to right itself usually. Tray applications such as Akregator and Amarok work best for this.