LT3081 Overload Recovery - Applies to Many LT308X LDOs

Here is a question that I received from a customer quite a while ago, but I will post the question here and then also post the answer since the question applies to multiple LDOs and I get similar questions frequently.  Here is the customer's question:

"I am using an LT3081 in an application and I have noticed that in an overcurrent situation the regulator seems to latch out and does not self-recover. I am using the DC1870A evaluation board. Is that normal operation for this regulator? I would expect it to limit the current at the maximum until the overcurrent situation goes away and then automatically go back to voltage regulation."