When you see the icon in the taskbar, try right-clicking it then select pin to the taskbar to keep it there. It should stay, whether it’s running or not.
Register Hereor login if you are already a member
You can open the 'Notification Area Icons', in the list of icons & notifications. it is supposed to appear in the taskbar where you can find applications names. Now you can select from the list. If you updated the system/ software this might be an issue.
When you are signed in to Skype, the Skype logo is displayed in the Windows taskbar. You can also see your Skype status icon displayed in the system tray at the bottom of your screen.
If you close the Skype window, the Skype logo and status icon still appear in the system tray.
To remove Skype from the system tray, right click the status icon in the system tray and select Quit Skype. This completely closes the application, which means you will no longer receive instant messages or calls through Skype.
You can change your settings so that when you close the application window by clicking X, Skype will keep running. This doesn’t sign you out, so you can still receive calls and instant messages while Skype runs in the background.
To do this: