The streaming restarts every time when you toggle the normal screen to a full screen as RadMediaPlayer gets removed from its current parent and placed inside a popup.
I suggest that you create a variable and store the position of RadMediaPlayer's MediaElement in this newly created variable. Then, you can hook on the RadMediaPlayer's MediaOpened event and update the position of the MediaElement everytime you fire the event.
In the attachment, you can find the latest RadMediaPlayer's dll along with the updated Fullscreen example.
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the Telerik team