I suspect its dust and the PC is running too hot.
To explain, some PCs keep the cooling fans going for a while when shutting down to make sure the components don't keep warming up when the PC shuts off. It sounds to me like that is what is happening. More dust means the temps will be higher and subsequently the fans will stay on longer till the temperature drops enough to allow shutdown.
I would go inside the PC give it a good clean and make sure all the fans are still running.