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This is likely a glitch in the software which will require a soft reset.
On your iPad, hold down the POWER and HOME button together until you see the Apple icon. After you see the icon, please release the buttons and the iPad will restart.
After the restart, try ending a new Skype call and it should work.
If the issue continues, please let me know otherwise if you can take a minute and use the rating system to rate our session as 3 stars or higher and press Submit so I am credited with helping you.