A follow up report:
I have had much more success using the shift-keypress-click method. I don't do it all the time, but whenever I have the problem where it's not remembering the shift, I'll do shift-keypress-click and it works more often than not.
I think some of my trouble may be related to static interference. I sometimes have erratic behaviour when returning to my desk chair because of its tendency to produce static electricity. I'm not shocking my keyboard (I'm super careful about that) but I do often do the "palm slap" to reset the keyboard and collapse any static buildup there may have been.
Oh, and it doesn't really seem to matter if I use the shift chord (my preferred method) or the shift key.
Thanks for the tips...