The Argument from Miracles is based first and foremost on the premise that there exist events which must be explained by supernatural causes - in short, some sort of god. Probably every religion has had miracle claims and so the promotion and apologetics for every religion has included references to allegedly miraculous events. Because it is likely that a god is their supernatural cause, belief in this god is supposed to be reasonable.
What is a Miracle?
Definitions vary, but two of the main ones I have seen are: first, something that is not naturally possible and so must have occurred because of supernatural intervention; and, second, anything caused by supernatural intervention (even if it is naturally possible).
Both definitions are problematic the first because it is practically impossible to demonstrate that something in particular cannot occur because of natural means, and the second, because it is practically impossible to distinguish between a natural and a supernatural event when both look identical.
Before anyone attempts to use the Argument from Miracles, you should get them to explain what they think a miracle is and why. If they cannot explain how it can be proven that a natural cause for an event is impossible, their argument wont work. Or, if they cannot explain how to distinguish between rainfall that occurred naturally and rainfall that occurred due to supernatural intervention, their argument is equally ineffective.
Even if we grant that a miraculous event is indeed exceptional enough to warrant an exceptional explanation, it cannot be assumed that this supports theism. We could, for example, postulate that the event was caused by the incredible powers of human minds rather than the incredible powers of a gods mind. This explanation is no less credible and in fact has the advantage that we know that humans minds exist, whereas the existence of a gods mind is questionable.
The point is, if someone is going to advance one supernatural, paranormal, or unusual explanation for an exceptional event, they have to be willing to consider every other supernatural, paranormal, or unusual explanation. The question which thus faces the believer is: how can one possibly compare all these different explanations? How on earth can one reasonably support the idea that something occurred because of a god rather than human telepathy or ghosts?
Im not sure that you can but unless the believer is able to show why their supernatural explanation is preferable to all the others, their claims fall flat. This cuts to the very nature of what a valid explanation is. When you cant show why your attempted explanation does a better job then mine, then you reveal that what you are saying does not really explain anything at all. It does not lead us to better understand the nature of the event and of our universe in general.
One problem for the Argument from Miracles is something which afflicts so many arguments for the existence of a god: it does nothing to support the likely existence of any particular god. Although this is a problem for many arguments, it does not immediately appear to be the case here - although any god might have created the universe, it seems that only the Christian God would likely be causing miraculous healings in Lourdes.
The difficulty here lies in the fact referenced above: every religion seems to make claims of miraculous events. If one religions claims are right and that religions god exists, what is the explanation for all the other miracles in other religions? It seems unlikely that the Christian God was causing miraculous healings in the name of ancient Greek gods at one time.
Unfortunately, any attempt to rationally explain away the miracle claims in other religions opens the door for similar explains in the first religion. And any attempt to explain away other miracles as the work of Satan simply begs the question namely, the truth of the religion in question.