I was just reviewing the datasheet for the LM317 and it lists the minimum load current as being 3.5 mA typical and 10 mA max. Based upon that number I don't think LM317 will work every time. since there is not enough current draw when the current is only 4 mA. Either that or it is right on the edge of operating. Am I looking at this correctly?

Hallo Joe,

you don't need to worry! The stuff with minimal operating current has to do with the output voltage regulating. It meens the following:

If you have a voltage regulator, that shall produce an output voltage of let's say +12V, then the regulator can only manage this, if a minimum output current of some mA is flowing. This is NOT a special disadvantage of LM317, but it's a standard phenomen of very most voltage regulators.
This cerrain behaviour is even mentioned in datasheet, but hidden between the lines! You will find it at specification of output voltage:

For LM7812C (National Semiconductors) output voltage is specified to be between 11.5V and 12.5V, if output current is between 5mA and 1A. Did you get it? The only meaning of this is, that the performance of regulator cannot be predicted if load current is smaller than 5mA!!!

What makes a regulator if load current falls below minimum current?
Output voltage rises, or by other words, differential voltage between input voltage and output voltage decreases. So, the regulator is no longer a regulator...

When I started with electronics I made some bad experiences with negative voltage regulators. If input voltage was at rather high levels and load current was even greater than this specified 5mA, at output a really dangerous voltage appeared, destroying some of my analog circuits. By the way, voltage regulator became abnormeously hot.

So, it can be wise, to garantuee, that even a higher minimum load current is flowing, than only this 5mA. This can be accomplished by a simple suited resistor connected from output voltage to ground.

Back to your question:
Adapted to your circuit, where the regulator works as current limiter: This regulation performance, where the regulator needs minimum current, must be taken into consideration, when the regulator works in the current limiting mode, means, if this calaculated threshold limit of 24.5mA is reached. It's THIS current, which must not fall below minimum current. So, if you would try to accomplish a current limit threshold of 3mA, for instance, then the regulator might fail. But with 24.5mA you are fine.

What makes the regulator, if current through it decreases below minimum load current? Nothing at all. Voltage drop across the current limiter circuit decreases to about 0.5V...0.7V. There seems to be a forward biased pn-junction, which lets the current pass. At 5µA I measured a voltage drop of about 0.6V. And, right, if you have a look at schematic diagram of LM317 in datasheet, you will notice a PN-FET (Q1), which lets the current pass through its source drain channel (looks like a low ohmic resistor). After flowing through this FET the current flows through two base-emitter junctions (Q3 and Q5). So, there's path from 'Vin' pin to 'Vout' pin of LM317, where the current can pass, resulting in a voltage drop of one forward biased pn-junction (like a diode).

If you want to measure the perfomance at very low currents, means with your bread board, then increase shunt resistor very much. If you use for instance 1MOhm and apply to the circuit 12V, then this voltage will drop almost totally across 1MOhm resistance. The difference between input voltage and voltage drop across 1M resistor is the voltage drop across current limiter.

Kai