If you're a B-theorist, it is no puzzle that the past can't change. It can't change because we are always in the same world, and so neither the past, nor the present nor the future can change. Today, let us suppose (I think correctly) that it is the case that on Wednesday it was raining. Could it tomorrow be the case that it wasn't raining on Wednesday? Not at all—for the very same world, the very same events, that make propositions true today is the one that we evaluate against tomorrow. The fact that the past can't change, thus, is a matter of mere logic—it just follows from the truth conditions for sentences.
But what if you're an A-theorist? So, you think that things will be objectively different tomorrow. Indeed, you already do think that some things about Wednesday will objectively change. For instance, while today (Saturday) Wednesday is objectively three days in the past, tomorrow it will objectively recede one more day into the past. So in fact we already have a change, but a change that the A-theorist doesn't mind. (Though she should.)
In any case, logic alone doesn't do the job. One way to see this is that some A-theorists actually think the future changes. Thus, today, it is false that either I am at Mass on November 8 or that I am absent from Mass on November 8. But come November 8, this disjunction will be true. But the clever tricks that open futurists use to make sense of an open future could be used, equally well, to make sense of an open past. (The parallel holds for B-theory. The B-theorist is committed to the claim that the future cannot change. This sounds fatalistic, but we must distinguish the ability to change the future from the ability to affect the future.)
In the setting of my earlier post on A-theory, the claim that the past cannot change corresponds fairly closely (and in fact exactly, if we assume a closed past) to the claim that the earlier-than relation is transitive. If today, a world where it rains on Wednesday is is past, tomorrow that world will also be past. So in the setting of that post, the explanatory challenge to the A-theorist is why the earlier-than relation E is transitive. The A-theorist who takes E to be fundamental can only say that it is a brute fact that it is necessarily transitive.
There may be A-theorists who can meet the challenge, however. Suppose that you think that there is a TimeShift operator which shifts tensed propositions time-wise. Thus, if p is the proposition that it is sunny, TimeShift(+1 day, p) is the proposition that in a day it'll be sunny. Suppose, further, we take worlds to be maximal consistent collections of propositions, or maximally specific consistent propositions. Then the TimeShift operator can also operate on worlds, and we can define E(w1,w2) to hold iff there is a t<0 such that w1=TimeShift(t,w2). Then it really is a matter of simple logic that E is transitive, and we have a perfectly good explanation of why the past cannot change.
Note, however, that an open-futurist cannot take this explanation. For her, the fixeity of the past remains a surd.
If this is right, then Tom Crisp is mistaken in taking the earlier-than relation between abstract times (which are just worlds in my terminology) to be primitive. An A-theorist should not say it's primitive—it needs explaining. Or at least I remember him taking it to be primitive, but my memory isn't so good.