You might want to use the Hide Object When setting to make your button disappear when conditions dictate that the popover should not be allowed to open. That will not only keep the popover from opening but provide feedback to the user that they can't open the popover before they try to by clicking on it.
Thanks for the suggestion, but in this case I am attempting to insert a custom dialog box to control access to the popover data with a simple challenge question (I don't need a high level of security, just a small control over who is accessing the data).
Then have the user click a regular button that opens that custom dialog. If the user gains proper access, use go to object to open the popover by assigning an object name to the Popover Panel (naming the button won't work).
Use True as the Hide Object When setting to always hide the popover button and put the regular button on top of it so that it looks like the popover button is extending out of the regular button.