jdhedden,
You do not say how far behind. Reading the docs:

NOTE 1: This higher resolution timer can return values
either less or more than the core time(), depending on
whether your platform rounds the higher resolution timer
values up, down, or to the nearest second to get the core
time(), but naturally the difference should be never more
than half a second.

It would not be unrealistic to see the times off due to rounding issues. Additionally, you do not specify which OS you are running Cygwin on. It is my understanding the granularity of sleep may be determined by the kernel. I was not able to reproduce your problem using the following code beyond the expected discrepency:

#!/usr/bin/perl
use strict;
use warnings;
use Time::HiRes 'usleep';

while (1) {
    print "Core : ", CORE::time, "\n";
    print "HiRes: ", Time::HiRes::time,  "\n\n";
    usleep (60_000_000);
}
[download]

Cheers - L~R