Hi Uwe,
sorry to hear that you suffer from the same problem.
Can you check if there are any errors in the JavaScript console (this link might help: http://codex.wordpress.org/Using_Your_Browser_to_Diagnose_JavaScript_Errors )
If that does not help, can you please try again after temporarily deactivating all other plugins and switching to the WP default theme Twenty Twelve? This is to rule out any interference from another plugin.
If that also does not help, I'd like to take a direct look at your admin area. In that case, please send me an email with the account info (my address is in the main plugin file "tablepress.php").
Regards,
Tobias