Ghazali, Biel, Malebranche, and Hume all deny that there is any necessary connection between natural 'causes' and their 'effects', or at any rate that we have any good grounds for believing in such necessary connections outside the mind with respect to natural phenomena. They take this to be an argument against the Aristotelian (and Lockean) contention that there are natural agents, endowed with essential causal powers, that produce effects in nature. The question is: in what sense are Aristotelians committed to the thesis that there are such necessary connections?

(a) It is admittedly necessary on the Aristotelian account that there cannot be transeunt action without an effect's being produced (or conserved). This is a conceptual claim having to do with the necessary connection between action and the production of an effect. However, this cannot be the target of the occasionalist and empiricist critique. Their target is not the claim that necessarily, if there are actions in nature, then there are effects produced; rather, it is the very claim that there is (or that we can know there is) action in nature.
(b) Since Aristotelianism as I have expounded it is compatible with the claim that some agents act indeterministically rather than by a necessity of nature, Aristotelians are not committed to the general claim that necessarily, for any potential agent A and set of circumstances C such that A is capable of producing effect E in C, A does produce E in C. (Free choice is an obvious counterexample according to most Aristotelians; and there is no reason for them not to admit the possibility of causal indeterminism in at least some sectors of nature.) Conversely, they are not committed to the claim that necessarily, if A has produced E in C, then A produced E in C by a necessity of nature.
(c) Even more striking, Aristotelians are not even committed to the claim that necessarily, if A produces E in C by a necessity of nature, then A's production of C was infallible (to use Hume's term), i.e. (?), unimpedible. For even if the water on my stove is now being made to boil by a necessity of nature, this might very well have been prevented by my taking it off the stove before it boiled or by the supply of gas being cut off, etc. That is to say, many deterministic natural tendencies which in fact result in natural necessities are such that it wouldn't have taken much power to prevent them from resulting in natural necessities. (This is a simple point that Averroes makes in his reply to Ghazali.) Even in the case of what I call in my paper strong deterministic natural tendencies, there is at least the metaphysical possibility that they might be thwarted by an omnipotent agent.
So the question remains: What is this necessary connection that is being denied by occasionalists and empiricists and is supposedly being affirmed by Aristotelians?

There are, I think, two possible answers:

(a) According to Aristotelians, there are natural (and not merely conceptual) constraints on what sorts of effects can be produced by given agents acting in given circumstances on given patients. These constraints are built into the natures of things (remember Suarez's talk of a cause's being proportioned to certain effects) and are at least in principle discoverable by experience and scientific inquiry. For instance, from what we know it is impossible that the flame on my stove should produce a personal computer when it acts upon the water in the kettle--or, to put it more neutrally, from what we know of the substances relevant to that situation, it is impossible that given just those substances, a personal computer should be produced. (This is not, by the way, to deny that a very powerful agent might be able to produce a personal computer in just those circumstances; it's just that such an effect could not be traced to the gas flame, water, atmospheric conditions, etc.) So on the Aristotelian view there are 'necessary', but more than merely conceptual, constraints (of the sort that occasionalists and empiricists are willing to admit) on what sorts of effects might be produced by given agents acting on given patients in given circumstances. This answer might be sufficent to shed light on many of the examples used by Ghazali and Hume (e.g., purgatives and the loosening of the bowels, billiard balls striking one another and motion of a given sort). Also, this answer has a clear connection with the essentialism which most occasionalists rebel against, according to which substances have natures or essences which are necessarily or at least immutably instances of natural kinds, which kinds themselves are necessarily or immutably connected with certain basic causal powers.
(b) A second sort of answer (and how exactly it is related to the first is open for discussion) is inspired by Ghazali's example of two identical pieces of cotton being exposed to a flame in exactly the same way. The claim is that the 'philosophers' are committed to a certain impossibility, viz., that the one piece of cotton should be consumed in the relevant circumstances and the other not. Now the first thing to notice is that this answer to our question concerns only a proper subset of instances of efficient causality, viz., those in which, according to the Aristotelians or 'naturalists', the effect in question occurs by a necessity of nature, i.e., results from a deterministic natural tendency.

Perhaps the best way to get at the claim that there are necessary connections of a special sort in such cases is to consider the following four propositions which, according to Ghazali, Aristotelians are committed to in their description of his example:
(1) Given the basic causal powers (BCP's) of this flame and this piece of cotton, along with various sine qua non conditions (e.g., proximity) for the flame acting on the cotton, there is at time t a deterministic natural tendency (DNT) toward the cotton's being being incinerated at t* (shortly after t).
(2) Necessarily, if there is at t a DNT toward the cotton's being incinerated at t* and if this DNT is not impeded before t* by another agent, then the cotton is incinerated at t*.
(3) Necessarily, a DNT can be impeded only by some agent's acting to produce some change in the causal situation or, to put it generally, only by some extraneous agent's counteraction.
(4) No agent impedes the DNT in question by an extraneous counteraction.
According to Ghazali, these are four propositions to which a philosopher (Aristotelian naturalist) is committed, and, as should be obvious, they entail
(5) The cotton is incinerated at t*.
But there are at least two objections, one philosophical and one theological: 
The philosophical objection is that we can easily imagine a situation which is observationally equivalent to the one which Aristotelians describe by means of (1)-(4) and in which (5) is false. Therefore, as far as we can tell, that situation is compatible with the falsity of (5) and the theory which describes the situation by appeal to (1)-(4) is mistaken in some way or other. Since (2) looks true enough given (1), and since (4) is simply an assumption made for purposes of argument, it must be that something is wrong with either (1) or (3). The ultimate problem seems to be either (i) the attribution of causal powers to things in the first place or at least (ii) the essentialism which rules out DNT's being impeded by an intrinsic alteration in the natures of the various agents and patients.
The theological objection is that we know from Sacred Texts that situations observationally equivalent to that which Aristotelians describe by (1)-(4) and in which (5) is false are not only imaginable but indeed actual. (Witness the three young men in the fiery furnace.) Once again, the diagnosis is the same.

NOTE: The medieval Aristotelians reply by holding onto (1) and denying (3), thus allowing for a different way in which a DNT (even a strong DNT) might be thwarted, viz., by an omission on God's part which does not alter the nature of any of the relevant things. Some contemporary naturalists (Harré and Madden) simply insist that even if (5)'s falsity in this case is conceivable, it is nonetheless impossible.