In that case, the parent process is not signalling your process and it dies when the parent dies. So you need to write a subroutine in C that sets a handler,

BOOL WINAPI SetConsoleCtrlHandler(
  _In_opt_ PHANDLER_ROUTINE HandlerRoutine,
  _In_     BOOL             Add
);
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and another that is called back. The handler routine can then issue a signal of its own for your perl program to trap. It's a bit of a maze but these are the set of functions you can choose from to manage the windows console: https://docs.microsoft.com/en-us/windows/console/console-functions

Update: If you can live with uninterruptable, you could also consider a DOS wrapper that does "START /B wrapper2.bat", where wrapper2.bat runs the perl program. This should then be detached from the console window.