It partly depends upon exactly what your graphic user-interface is set up to do (and how much support for, e.g., “button groups” you have at your disposal with any particular platform), but here is a general strategy for the handler for a button that will take a little while to complete.   (Entirely-abstract non-Perl pseudocode):

   disableButton();
   try {
      doTheWork();
   } 
   finally {
     enableButton();
   }
}
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Translating that to “Perl or what-have-you” I leave as an exercise to the reader.   The try..finally construct that I refer to (which doesn’t automatically exist in Perl) is one that will always execute the finally portion even if an exception occurred.

My point, in using it, is that you always have to anticipate and to handle exceptions that may occur in your button-handler, so that you always re-enable the button.

Some GUIs provide for button-groups which simply means that the outer-level framework takes care of enabling and disabling the buttons.

Likewise, some GUIs implement buttons as objects that automatically handle the disable/enable logic (and exception-trapping), calling an onClick method of some kind to doTheWork().