Sub theme by default inherit the screenshot from base theme.You can override the screen shot by simply adding screenshot of your sub theme in your sub theme directory
The optional screenshot key tells Drupal where to find the theme's
thumbnail image, used on the theme selection page
(admin/build/themes). If this key is omitted from the .info file,
Drupal uses the "screenshot.png" file in the theme's directory.
Use this key only if your thumbnail file is not called
"screenshot.png" or if you want to place it in a directory outside of
your theme's base directory (e.g. screenshot = images/screenshot.png).
screenshot = screenshot.png
Other things which may help.
As Jhilke comment try clearing your caches.
Check the screenshot file permission it should readable by web-server.