My suspicion is that you've written or downloaded a function with the same name as one of the functions included in MATLAB that is used to open the Variables window when you double-click on a variable in the Workspace desktop component.
Look at whatever functions you wrote or downloaded or whatever add-ons you installed between the last time you were able to successfully open a variable by double-clicking and the first time it failed. If none of them seem to match a function in MATLAB, either show the list of function names here or contact Technical Support and work with them to determine what's preventing the Variables window from opening.
