I, too, have experienced spinning beachballs and application quits while using PanX. However, I have never had to restart my computer to bring up PanX again. Unfortunately, my experiences do not exactly match anything described above.
Here is something I have noticed recently on my computer that may be able to be replicated on other computers: I have gotten the spinning beachball numerous times, using widely different databases, while scrolling through the Automatic Form Construction instruction under the Help menu.
Do this: Open up any PanX database. Under the Help menu, select Panorama X Help. Then select "Automatic Form Construction" from the list of terms and topics. When the instruction is present, scroll down using your finger on the mouse (not the scroll bar). Sooner or later (probably later) the spinning beachball will appear.
This first occurred, while reading the instruction, with a newly imported database of 33,788 records open. I thought the number of records may be causing PanX to slow down while scrolling over the animated GIFs; but, this does not seem to be the case. I have gotten the spinning beachball to appear using six different databases of varying sizes.
The spinning beachball has also appeared with no databases open. This is the "No Windows" condition described elsewhere. Interestingly, the ball can easily be stopped by moving your cursor over the PanX icon in the dock.
In situations with a database open, the ball can usually be stopped by clicking - several times - on the desktop and/or the data sheet (if open). If that fails, a Force Quit may be necessary.
This all happened on an iMac running OS X Yosemite, version 10.10.5. with the latest version of Pan X.