Wolfgang,
I have not seen this issue previously. Odd problems are often resolved by simply re-installing the product. If you are comfortable with that process, I would recommend trying that first. Diving in to the logs could lead to an answer, but it may take a while.
If you do not wish to re-install, and would like to troubleshoot :
Can you take a couple of screenshots showing when exactly this happens? Is it when you close the graphical interface to the program? or is it when you exit pgp services? Or just when shutting down the computer?
Would you mind genearting some logs for us to review?
Please follow this guide to enable debug mode. That will allow you to create some logs, and those may lead us to better understand.
Enable debug level logs for PGP Desktop on Mac OS X
http://www.symantec.com/business/support/index?page=content&id=TECH148947
Thanks,
Phil