What would explain urine that resists freezing?
Urine is an aqueous solution of urea, uric acid, sodium salts and whatnot. These solutions usually exhibit freezing-point depression. 

As Brian has correctly pointed out in a comment, the effect isn't that strong and a quick and dirty look in the literature shows that a freezing point around -1.3 to -2.2 °C. 

You might want to try a cooling bath with dry ice in isopropanol or acetone or other drastic methods to achieve shock-freezing.