Shell buffer processes all die when I run "man"

[David Karr]

I'm using Emacs 24.5.1 in Cygwin on Windows 7.

I create multiple shell buffers (using a wrapper package that I
wrote).  I've used this basically unchanged for more than 10 years.

I recently noticed that if I have one or more shell buffers, and I run
the "man" function, I often see a short message saying "Waiting for
process to die", and then I see that all of my shell buffers say
"Process shell hangup" (or "shell<1>", depending on the buffer name).
I've been seeing this consistently for several weeks now.

I haven't updated Cygwin recently.