Retract an already submitted recommendation letter (written for an undergrad student)
I think you should do nothing.
(Nothing with respect to the letter, that is. You may of course want to consider intervening with the student as you would with any other student whose performance suddenly drops off. As Azor Ahai says, he may be experiencing some sort of academic or non-academic problem.)
By putting my name on the letter I effectively vouched for him and his ability to perform at a certain level. To me, it's as if I made a promise to the other university, but now I see that I misled them (albeit unintentionally).
I don't see it that way. You couldn't possibly make promises about his future performance, and the receiving university will not have interpreted it that way. They are well aware that "past performance is no guarantee of future results". Provided you made an honest assessment based on what you knew at the time, your letter was in no way misleading, and you have no obligation to correct it.
Proactively sending a followup unrecommendation would come across as somewhat vindictive, and I think it's sort of an ethical gray area. The student consented to having you send a letter, sharing his academic progress, at a particular time; I think it's a little questionable whether that consent extends to having you send additional letters. (However, if the other university should contact you to ask about him, I do think it would be appropriate to give them an update on his more recent work - but to me that feels different.)
That said, I don't think the student is really likely to profit from this anyway:
Your initial letter, saying "I've known him for half a semester and so far he's doing fine in this one class", can't really have done much good for his application in the first place. If the other university is "much stronger", having such a letter, in place of a very positive letter from someone that knew him well, may have sunk his application from the outset.
If he does receive an offer of admission, it will almost certainly be contingent on continued satisfactory academic progress. The other university will review his final transcripts before he actually starts in the program. If he receives a poor grade in your class, they may very well revoke his admission. Indeed, discussing this possibility with the student may encourage him to shape up.
Based on your statements, all that you vouched for is the performance of the student at that point in time.
What confidence can you provide in the new behavior of the student being his "true" character (rather than a sign of an unknown external pressure)?
In what way would you retract your letter that will not cause you to appear as being vindictive?
What reason can you give to retract your letter that is not covered equally if not better by the outcome that this student is on track to earn a lower final course grade on his transcript?
With so many unknowns, your first instinct should not be to retract the letter.
When you care first to know why the behavior has changed, call the student for a visit and give him a chance to explain why.
When you care first not to be seen as vindictive, call the student for a visit, explain to him that you face such a decision, and give him the chance to defend himself.
When you want nothing less than a recognition that your letter then was only for his performance at that point in time, allow the student now his time to complete his own record of his performance past that point.
To conclude, this link from an article in Psychology Today Jan 2013 also provides background for my summary of the opening statement to relate current behavior as a predictor of future behavior. Other citations could likely be found branching from this.
A recommendation letter is/should as close as to your perception of the truth as possible as to the time of writing.
If you have sent it, retraction would be inappropriate (unless you got notice that the student achieved his marks by cheating).
Of course, a future recommendation letter may be not that brilliant, and you should let the student know that you'd rather not send another one if he asks you for it.