Richard Hennessey has an interesting post on Aquinas's Third Way, in which he discusses the first part of the argument, on 'possibility to be or not be'. The Third Way is tough going, plain and simple: it is the most confusing of the Five Ways; it uses the least intuitive technical terminology; it has manuscript variants on a crucial premise; Thomists have usually only explained it in the vaguest terms; and as for critical studies of it -- if you look at what has been published on the Third Way, you have in hand proof that a veritable ocean of truly awful philosophical papers have been published in the past hundred years. But there are things we can do to clarify matters, and I think when we take them into account we see that Richard has been somewhat misled by the terminology used in the argument, and therefore wandered into the wrong system of modality. It's a common confusion.
The Third Way claims to be about possibility and necessity, and it is, but when we think of possibility and necessity, we tend to think of diamond and box -- i.e., possibility and necessity as usually found in standard modal logics, in which possibility is represented by a diamond or lozenge operator and necessity is represented by a box or square operator. Moreover, we tend to think of it in alethic terms; e.g., when we think of necessity we are not usually thinking of necessity in the sense of 'necessary from the perspective of doing one's duty'. This sense of modality abstracts entirely from questions of time or causal power and is based entirely on considerations of consistency. This sense of modality is not in view here. I have seen it claimed on the basis of passages like the Third Way that Aquinas's view of alethic possibility and necessity implies that if something never exists it is not possible; this is definitely false. Aquinas is quite clear that 'possibility' and 'necessity' are not univocal terms, and one of the senses he recognizes is pretty much our standard alethic notion, based wholly on considerations of consistency. But there is another sense, and it is the one operative here; in this sense something is said to be possible in light of (in the words of the commentary on Aristotle's De Caelo) "what is, or is not, within the power of an agent or patient." We know that this has to be the sense here because it is the sense of possibility that is used in Aristotelian accounts of generation and corruption, and the Third Way explicitly appeals to generation and corruption.
We use our senses to interact with the world, and we reflect on what we learn in this way; when we do we recognize that some things are generated and corrupted. That is, they begin to exist and they cease to exist. This shows that they are capable of being and not being. But this capability is not an abstract sort of capability; we do not learn merely that their beginning and ending is not internally inconsistent. Rather, we learn that things have a power for being and not being; or, in other words, they have an actual ability to exist for a duration. Prior to their beginning to exist they have no actual ability to exist for a duration because they don't exist, and therefore there is nothing to possess this ability. After they cease to exist, there is also nothing to possess this actual ability. Therefore things don't have the actual ability to exist for a duration outside the limits of that duration. Therefore, from studying generation and corruption in the world we learn not merely that things can be and can not be; we learn that there are things that by their own nature and circumstances have the ability-to-be-and-not-be.
Now, if something genuinely has the ability-to-be-or-not-be in this sense, there must be some time at which it exists and some time at which it doesn't. If there is no time at which it exists, it only has the ability not to be, and this means that it is not possible in the relevant sense. If there is no time at which it does not exist, it only has the ability to be, and this means that it also is not possible in the relevant sense. Therefore when Aquinas says, "what is possible not to be at some time is not," he is not saying something strange or controversial; it is necessarily true on the conception of possibility that is being used in the Third Way.
It's also clear here that it's not quite true to say, as Richard does, that "Aquinas has here, that is, identified modal 'logic' with temporal 'logic.'" There would be nothing wrong with this in general, because any temporal logic is in fact simply a modal logic in which possibility and necessity are given temporal rather than alethic interpretations. But it's not quite what's happening here. He is not conflating alethic and temporal modalities. He is appealing to a modality; but it is, we might say, a causal modality with a temporal component, one that has actual use in discussion of generation and corruption (Aristotle uses it extensively in the treatise On the Heavens). Because of this, it isn't an ad hoc modality; an Aristotelian has a principled account of why it is needed: it is presupposed by certain kinds of explanations of certain kinds of natural phenomena. And because of this the entire part of the argument that Richard discusses in his post is actually unexceptionable. I never know what Richard means by 'evidently sound' since 'evidently' is a psychological term and what is 'evident' will obviously vary from person to person; I doubt Aquinas himself would think (or care) that any of the Five Ways are 'evidently sound' if it means that they would be evidently sound to everybody. Certainly there is nothing about the Third Way that will be 'evident' to most people. But the part that Richard discusses in his post is the part of the argument in which Aquinas merely (1) points out that a certain kind of modality is used in explaining generation and corruption; and (2) establishes what follows from this modality by definition.