Good news! We found the call to set the delay has a max somewhere between 5000 and 10000 on the affected systems. So the workaround, which is working: 
our $isleep = 15;  # Number of seconds to sleep between iterations
{
    my $counter = 0;

    sub Callback_Running {
        my($Event, $Context) = @_;
        if(SERVICE_RUNNING == Win32::Daemon::State()) {
            $counter += 5;
                print $fh $counter . "\n";
            if ($counter >= $iSleep * 60) {
                print $fh "Checking in.\n";
                # do stuff;
                $counter = 0;
            }
            $Context->{last_state} = SERVICE_RUNNING;
            Win32::Daemon::State( SERVICE_RUNNING );
        }
    }
}

[download]
However, resume after pause still does not work 
C:\Users\john\test>net continue TestService
.
The Test Service (TestService) service failed to resume.

More help is available by typing NET HELPMSG 3538.

[download]

After pausing Repeated messages "The Test Service (TestService) service has reported an invalid current state 0." in event viewer. Continue does not work.

In reply to Re^6: Win32::Daemon service doesn't reach RUNNING state by SwaJime
in thread Win32::Daemon service doesn't reach RUNNING state by SwaJime

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