hpqtro08.exe is the HP status monitor for HP printers in the toolbar by the clock. my fist suggestion would be, if you don't use it just disable it, it's not an essential thing to have running, it just gives you slightly quicker access to the HP tools.
If you do use it then I'd go for getting the latest software from the HP site for your printer, remove the current software and install the new version. If that still doesn't sort it then it's possible to increase the time the system will wait for the program to shutdown before giving the error.