As it happens, I used brute force and figured out the problem.  It took a while, but I was right: Poser "remembered" the window in a place that is one pixel away from being inaccessible on the "wrong" monitor - the secondary rather than the primary.  I dragged the window out and now we are back in business!

Again, it sure would help if Poser had a factory reset.  It's too easy to drag some window into a bad place. 

My friend, I will make sure I copy down your great advice!  I solved my own problem this time after taking a long time to work it out for myself.  Next time, I may not be so lucky.  I will try it out and hopefully it will work as you say!  That would be a big help indeed, and I thank you for looking in on my issue.