After exiting a process that returns me back to the shell, my prompt text is hidden. (Example - emacs file.txt; or ssh myserver.com; then exit. From then on, prompt text is hidden.) The characters are passed: when I type blindly and hit enter the command goes through, but I cannot see what I am typing. My fix has been to simply close and re-open a new cygwin window. 
 
I experienced this many years ago and found a fix. I recently got a new computer but quite unfortunately I do not remember the solution, and searching both my personal archives and the internet at large turned up nothing.