I am not sure just when AMHR closed--they did have an open registration for a long time, and then it closed and only hardshipping was allowed--I am pretty sure that hardshipping was available when I first got into Minis, in 2001, but I didn't pay much attention to it--I remember being relieved that I could get my one and only AMHA mare her R papers for only $50 at the time, instead of having to do a regular hardship. Then that hardshipping closed, and again, not sure what year that was, but I would say about 10 years ago? Since then only horses that already have ASPC, AMHA or Falabella papers can be "hardshipped".
AMHA had open hardshipping for any horse 34" and under up until December 31, 2013. Now that is all gone, so to get AMHA papers you must have a foal with two AMHA registered parents.