What would explain urine that resists freezing? A frozen urine specimen is required for an organic acids lab test, but the urine refuses to freeze after 4 days in a regular freezer turned as low as it will go. What would explain this, and how cold might it need to be to freeze?
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.