Rich is right that you already have a really good overall score so you should fare well at the top schools, assuming that everything else in the application looks good.
I am not an admissions person so I don't have the specific insight that an admissions person might, but in knowing several admissions people what I would say is this:
While your overall score is amazing, admissions people do seem to say that the committees take a close look at that Quant score to make sure it is up to snuff. 44 is still a very good Quant score but if you think you have the potential to score higher it might be worth retaking. Even if the overall score goes down, my understanding is that while admissions committees are not going to "superscore" your GMAT score, they will see that higher Quant score and probably give you credit for it while still taking the higher overall score.
There doesn't seem to be much of downside to taking the GMAT multiple, multiple times. I have seen people get into top top programs after taking the GMAT 5 or 6 times and I even once tutored a guy who was told by someone on the admissions committee at Columbia to just take the test one more time (he had already taken it 3 times) to try to get a better score and to show the admissions committee that he wanted it bad enough that he was willing to do it. He had a connection to this particular admissions person so I am not saying that his situation is typical but in the end he did get in.
So I think that if you believe there is a good chance that you will score better (as judged in part by official practice tests) then I would probably try again.