Hey Julia,
Thanks for the question. Since there is no agreed upon, unambiguous definition for what a “friend” is, we don’t quite know what we’re asking when we say “is this person still a friend?” or “is it true that friends should keep appointments?” Our brains like to categorize (friend / not friend) but taking these categories too seriously can lead us into trouble. So, for clarity sake, I think it’s best in this discussion to replace the word “friend” with what we really mean by it.

Should you consider this person less reliable than you did before they canceled three times in a row? Absolutely.
Do you still have positive feelings towards this person? That depends on how much those three cancelations bother you.

In my view, “sufficient processing” in this case would imply that you now think it more likely than you used to that this person isn’t enthusiastic about seeing you, and you think it is more likely than you used to that this person will cancel future plans. You may want to then analyze more deeply to try to figure out if it’s really the case that they don’t want to see you very much, or if it is more about them become flakier in general. Or whether it could just be unfortunate luck.

At that point, I think it would be good to decide whether you still think it’s worth it to you to try to make further plans with this person, or maintain a close bond with them, given the new information you have learned.

“If a friend cancels plans on you three times in a row, and you didn’t anticipate that they may cancel that third time, you failed to sufficiently process the first two occurrences.”

Perhaps I should not be surprised at the third cancellation, but I would certainly be disappointed. As a practical matter, how would you suggest a person change her model based on data such as this? For example, should she:

Revise the belief that the individual is her friend?
Revise the belief that friends should keep appointments?
Revise the belief that friends do keep appointments?

None of these seems particularly satisfying or convincing to me. Can you give an example of a reaction to this information that would constitute “sufficient processing,” and a way in which it could be translated into productive action? And what is your take on the distinction between surprise and disappointment?