This is a phenomenon you see often amongst Christians, particulary the more pietistic variety. When they see a contentious debate, for example over some nuance of Christian theology or praxis, they might say something like: "I know how you can end this debate. Why don't each of you get on your knees and pray to God that the Holy Spirit will reveal to you the correct position to take on this issue? If everyone did this, then we would all know the right answer."
Even beyond the Holiness-inspired anti-intellectualism of the idea, it's just plain wrong - and poor theology to boot.
First, the Word of God is the normative principle by which matters of doctrine and practice are decided, not the subjective impressions we may feel and attribute to the Holy Spirit. There are a few narrative passages in the Old Testament that describe priests or prophets consulting God directly for instructions in specific situations, but never is this practice commended as normative. On the other hand, there are numerous times in which Jesus or an apostle appeals to the Law and the Prophets - the written Scriptures - as the authority to follow.
The London Baptist Confession states about the interpretation of Scripture:
The Holy Scripture is the only sufficient, certain, and infallible rule of all saving knowledge, faith, and obedience, although the light of nature, and the works of creation and providence do so far manifest the goodness, wisdom, and power of God, as to leave men inexcusable; yet are they not sufficient to give that knowledge of God and his will which is necessary unto salvation. Therefore it pleased the Lord at sundry times and in divers manners to reveal himself, and to declare that his will unto his church; and afterward for the better preserving and propagating of the truth, and for the more sure establishment and comfort of the church against the corruption of the flesh, and the malice of Satan, and of the world, to commit the same wholly unto writing; which maketh the Holy Scriptures to be most necessary, those former ways of God's revealing his will unto his people being now ceased. . . .
All things in Scripture are not alike plain in themselves, nor alike clear unto all; yet those things which are necessary to be known, believed and observed for salvation, are so clearly propounded and opened in some place of Scripture or other, that not only the learned, but the unlearned, in a due use of ordinary means, may attain to a sufficient understanding of them. (LCF 1:1,7, emphasis added)
What are "the ordinary means"? Study, research, hard work, proper hermeneutics, other tools of that sort. Yes, these would include prayer for wisdom, and an open heart and teachable spirit that is ready to submit to the commands of Scripture. But prayer, in and of itself, is not the ordinary means by which we come to a correct understanding of God's Word.
Imagine, for example, that a well-known Bible teacher wrote a commentary on one of Paul's epistles, and he continually appealed to arguments like this: "When Paul wrote such-and-such, this is generally taken to mean x, but I prayed to God and the Holy Spirit revealed to me that Paul really meant y." Who would take such a commentary seriously? It would be grossly irresponsible for a reputable publisher to even accept a manuscript that appealed to this kind of reasoning. Yet, it seems, as long as the dispute remains unpublished and a non-scholarly dispute between fellow Christians, this kind of thing becomes perfectly acceptable. There is not one standard for professional theologians, and another for amateur Bible students.
Second, it is a purely subjective criterion, and as such it completely defies verification. Suppose that to the above, I responded: "I did pray about this, and the Holy Spirit revealed to me that those who disagree with my position are the most wicked heretics alive, and I ought to tie them to a stake and burn them to death." There are those who will scoff at this, and who will berate me for making such a tasteless joke. But that's just the point. How do they know it's a joke? After all, they cannot read my mind, so they have no empirical evidence that the Holy Spirit didn't command me to put heretics to the torch. Furthermore, there are plenty of examples in Scripture of God commanding his faithful people to put his enemies to death, so they can't claim my "revelation" is unprecedented, either. "But God just doesn't want people to behave that way," my opponent protests. I shrug. You have your subjective impression, I have mine, and we're no closer to an answer to the debate than we were before.
Most fundamentally, I think that 99% of the time this kind of argument is a "sanctified" argumentum ad verecundiam, the appeal to authority. When someone claims that "I prayed, and God revealed to me x" (where x is some controversial position), it implies: "God told me x. You don't want to oppose God, do you?" Well, if "God" apparently stands opposed to the use of right reason and the "due use of ordinary means," I guess I do.
Postscript: In the comments, Tom Harrison asks a good question: "But isn't citing Scripture also an argument from authority?" Yes, it is, but it is not a fallacious appeal to authority. First, in a dispute between fellow Christians, in theory there should be no dispute about the authority of Scripture. It is an appeal to an authority that both parties accept as authoritative. Second, Scripture is an objective authority that is equally available to any party in the dispute. You can't say that about the subjective impressions supposedly given by the Holy Spirit to a person; since they cannot be verified objectively, they are of dubious authority. Not all appeals to authority are fallacious; I submit that appeals to a subjective experience are, and I could have made that more clear. Good point.