This is what I get in the terminal:
kile(5347)/kdecore (KLibrary) findLibraryInternal: plugins should not have a 'lib' prefix: "libkonsolepart.so"
kile(5347)/konsole Konsole::Session::run: Attempted to re-run an already running session. 
The program 'kile' received an X Window System error.
This probably reflects a bug in the program.
The error was 'BadWindow (invalid Window parameter)'.
  (Details: serial 8519 error_code 3 request_code 20 minor_code 0)
  (Note to programmers: normally, X errors are reported asynchronously;
   that is, you will receive the error a while after causing it.
   To debug your program, run it with the --sync command line
   option to change this behavior. You can then get a meaningful
   backtrace from your debugger if you break on the gdk_x_error() function.)
kile(5347)/konsole Konsole::SessionManager::~SessionManager: Konsole SessionManager destroyed with sessions still alive 

Reproducible: Always