'I', writes Barthes, 'is not an innocent subject that is anterior to texts. . . . The I that approaches the text is itself already a plurality of other texts, of infinite or, more precisely, lost codes (whose origins are lost).'
The importance of authorial intention (hereafter AI) to some people obviously stems from a desire to safeguard interpretation, from the dangers of an anything goes 'relativism'. In this line of thinking, meaning is not created by readers but is embedded in the text by an author. The task for the interpreter then is to discern what the original author intended and to use this as a criterion for adjudicating proper interpretations.
While this is a most noble task, and one that I have often subscribed to in the past (and still slip into in moments of rhetorical weakness), it is I would suggest, at the same time, an inexact one. Let us take for example Paul's letter to the Romans. After centuries of intense study, scholars cannot agree as to whether Paul wrote to Jews, to Gentiles, or to both; depending on which group one thinks the author addressed, scholars have come up with any number of reasons why Paul sought to address them. If these basic questions of 'intention' cannot be settled, how is 'AI' going to arbitrate between these subtleties. The affair ends up being quite circular.
I think authorial intention is misguided as the sole retainer of meaning for a number reasons:
The notion of meaning that results from a strict adherence to AI ends up resorting to a pre-linguistic meaning, meaning is something which the author wills. Terry Eagleton states:
It is as if meaning is a ghostly, wordless mental act which is then 'fixed' for all time in a particular set of material signs. It is an affair of consciousness, rather than of words. Quite what such a wordless consciousness consists in is not made plain. Imagine looking up from the text, and mean something, is the meaning any different from the words that express it? 
Here I quote Eagleton because he will say it so much better than me!
Even if critics could obtain access to an author's intention, would this securely ground the literary text in a determinate meaning? What if we asked for an account of the meaning of the author's intentions, and then for an account of that, and so on? Security is possible here only if authorial meanings are what Hirsch takes them to be: pure, solid, 'self-identical' facts which can be unimpeachably used to anchor the work. But this is a highly dubious way of seeing any kind of meaning at all. Meanings are not as stable and determinate as Hirsch thinks, even authorial ones - and the reason they are not is because, as he will not recognize, they are the products of language, which always has something slippery about it. It is difficult to Know what it could be to have a 'pure' intention or express a 'pure' meaning; it is only because Hirsch holds meaning apart from language that he is able to put trust in such chimeras. An author is translated and variously interpreted just like any other.
Another reason I feel AI is misguided is because it assumes that if the author is not the determiner of meaning, then the text can mean anything. Eagleton humorously calls this fallacy the argument from the floodgates. He rants:
Once you allow one person to be sick out of the car window without Imposing a lengthy gaol [jail] sentenced then before you know where you are motorists will be throwing up out of their vehicles all the time, and the roads will become impassable.
This fallacy is often invoked after a detractor of 'AI' has just spent considerable words on the deficiencies of 'AI', in which the defender of 'AI' cheekily muses about the detractors intentions.
It is true that I desire my own work to be understood and hence I do show an interest in 'AI' after all (although my grammar at times precludes this possibility). The wrong assumption, however, is that without 'AI' readers can make texts mean whatever they like. There are still good interpretations and bad ones. Even to ones detest, writing is like giving birth, and once the text is severed from the umbilical cord it is no longer our own. We simply offer it to the world and see if it convinces anyone. If it convinces many, it might even become a consensus (although consensuses never seem to last long). The adjudicators of good and bad become what Stanley Fish calls our interpretive communities.
My final remark is that what one sees depends primarily on where one stands. There is no known way to shed our selves from our social contexts. We can not pick ourselves up by our bootstraps up to Olympian heights so as to get the objective view of what the author meant. This is even more precarious when the author is dead, and cannot answer our queries.
I offer this in humility believing in a God who makes meaning possible, but conceding that meaning is not a possession, 'For now we see in a mirror dimly.'
 Roland Barthes, S/Z (New York: Hill and Wang, 1974), 10.
 Terry Eagleton, Literary Theory: An Introduction (Minneapolis: University of Minnesota Press, 1983), 67.
 Eagleton, Literary Theory: An Introduction, 69.
 Terry Eagleton, After Theory (London: Allen Lane, 2003), 205.