Most of the time when a Protestant criticizes a Catholic practice, the criticism is not only based on a caricature, but more noteworthy is the fact the criticism contains an unparalleled level of irony. When it comes to the subject of Intercessory Prayer, both of these elements are present.
When I've talked to Protestants on the matter, the fundamental problem they have with Intercessory Prayer is that they envision it as living people on earth talking to unconscious people, without realizing the Protestant themself has unconsciously made the assumption that the saints in heaven must unconscious. Luther was actually more consistent here than other Protestants, since there is good reason to believe he held to something called "soul sleep," in which the soul does not go to Heaven after death but instead "sleeps" in an unconscious state at the graveyard awaiting the Resurrection. From that perspective, it makes perfect sense to say a soul that is "sleeping" and not in Heaven also cannot hear prayer, and it also makes sense at that point to deny the notion of Purgatory. But once the heretical notion of "soul sleep" is addressed, then the caricature is also addressed.
Now onto the irony behind the Protestant criticism of Intercessory Prayer. It turns out that with all the brouhaha over whether a saint in Heaven can intercede for a Christian on earth, the Protestant has failed to realize that Protestantism rejects the most important intercession of all, the Intercession of Jesus before the Father. This will be the focus of my post as I go onto explain.
The Protestant doctrine of Faith Alone holds that justification is a one time event involving the imputation of Christ's righteousness in which God sees Christ's righteousness instead of our unrighteousness. At that moment God declares that all the past and future sins of the believer are forgiven, with no requirements left preventing the believer from entering heaven. If only this were true.
The fact is, Scripture never speaks of future sins being forgiven, only past sins, which is why someone has to repent each time they sin (e.g. David, Peter). Indeed, one of the most devastating passages in all of Scripture for Protestants (especially Calvinists) is Mark 11:25,
Whenever you stand praying, forgive, if you have anything against anyone, so that your Father also who is in heaven may forgive you your trespasses.
This verse shows that the Christian must regularly ask for forgiveness of whatever sins they've committed recently and that if they don't forgive others then the Father wont forgive them. This verse alone brings down Faith Alone theology and leaves Calvinists scrambling for the some of most embarrassing excuses I've ever seen. For example, Calvinist scholars have said these kinds of passages are not talking about actual forgiveness taking place, but rather about how a Christian can "feel good" knowing their sins are already taken care of.
But to turn up the heat even more, consider the following passages talking about Jesus' intercessory role in the forgiveness and salvation process:
Hebrews 7: 23 The former priests were many in number, because they were prevented by death from continuing in office, 24 but he holds his priesthood permanently, because he continues forever. 25 Consequently, he is able to save to the uttermost those who draw near to God through him, since he always lives to make intercession for them.
Romans 8: 33 Who shall bring any charge against God's elect? It is God who justifies. 34 Who is to condemn? Christ Jesus is the one who died - more than that, who was raised - who is at the right hand of God, who indeed is interceding for us.
1 John 2: 1 My little children, I am writing these things to you so that you may not sin. But if anyone does sin, we have an advocate with the Father, Jesus Christ the righteous. 2 He is the propitiation for our sins, and not for ours only but also for the sins of the whole world.
These passages are all speaking of Jesus' intercession in the present tense. The Greek verbs are in the present tense, meaning that the action is not a one time event of the past, but rather is taking place right now. But how can these passages speak of Jesus interceding for us in the present tense if our sins are already forgiven at the moment of conversion, as Faith Alone teaches? That's impossible, and thus by affirming Faith Alone the Protestant has unintentionally denied Jesus' role as Intercessor.
In desperation a Protestant might respond by saying these texts are not speaking of forgiveness of sins or justification or something like that, but as I said this is sheer desperation. Not only is such a response completely ad hoc, even worse is the fact these passages are clearly given within the contexts of the High Priesthood, justification, forgiveness, etc.
I cannot think of much more to say other than that this is one of the most devastating arguments a Catholic can use against a Calvinist, and it's abundantly clear which side is truly following Scripture.