Thunderbird not closing properly

Many times I have found that when I launch TBP I get a message saying TB is running but not responding. This is when I have been using TBP then closed it. It seems that the window closes (it is not minimized and not visible on the Applications sheet of Task Manager) but does not shut down TB (it is still visible in the Process sheet).

I'm not sure when this started, it seems to have been with TB 6.