not to be found on the Cisco site, not even in PoE troubleshooting guide a minimum is mentioned, but not the value!
as this post at het Texas Instruments site it may be 10mA
To clarify, did you attach this 1kohm resistor to the output of the PD (VDD-RTN) or on the output of the converter? You will need to reduce the resistor value until 10mA is the input current draw.