The issue is that you only search for the window once. $window[0] doesn't automatically update as the window state changes. You need to test each time through the loop. The test code cleans up a little by putting it in a sub:

use strict;
use warnings;
use Win32::GuiTest;

while (my $window = findWindow("Calculator")) {
    print("calculator window is open\n");
    sleep 2;
}

print "Calculator window closed\n";


sub findWindow {
    my ($caption) = @_;
    my @windows = Win32::GuiTest::FindWindowLike(undef, "Calculator");

    return $windows[0];
}
[download]

Prints (for my test):

calculator window is open
calculator window is open
calculator window is open
calculator window is open
Calculator window closed
[download]