If someone bids higher earlier in the auction (such as the two to three days of which you spoke), that person will win, because he bid the highest. That is how auctions work. The point here is that you have no way of knowing what his high bid (proxy bid) really is; you only know that he bid at least enough to be on top. For example, in a seven-day auction, if bidder A bids $42 on day one and bidder B bids $75 on day three, while the auction is still going on you will see bidder B listed as the high bidder, but at $43, which is one bid increment over the next-highest bid of $42. You know that B bid more than A, but you do not know how much. If the auction ends like that, B will win for the same $43 price and you will never know what his max really was.
Let us say that bidder C comes along on day five and bids $61. Bidder B will still win, but he will be listed as winning for $62, since much more of his proxy bid was used up to keep him as top bidder, by placing him one increment (in this case, a dollar) above the second-highest bidder, C.
What happens is that people such as yourself, many of them new to eBay and/or AS, do not fully understand how eBay's proxy bidding system works. Frequently new AS members come in here, claiming that the winning bid never appeared during the auction, only to show up after the end, posted as hours or days before. (If you were to do a search of these forums, you would probably finds dozens of posts similar to yours.) The reality is that the bid did indeed appear during the auction, when it was originally made, but since its amount was lower than your snipe, you did not take notice of it. For example, if you had a $25 snipe scheduled, you were not concerned about a $6 high bid going into the last hours of the auction, because you were confident that your powerful $25 would easily trump the paltry $6 figure. But what you did not realize was that the $6 bid, high bid at that time, was actually only part of a much higher proxy bid, greater than your own snipe, possibly much greater. The result is that that highest bid always wins, even though it was made days before.
Finally, I wish to caution you against allowing others to decide an item's value to you. You mentioned researching how others bid and speculating what their final bid amounts will be. While it is good that you are aware of your competition, the result ends up that your snipe amount is to some degree determined by what you think others will bid for it. Part of the point of a snipe is to set the absolute max that you are willing to pay, then walk away and let AS place the bid for you. You will only get one chance, so place the bid at the level you are prepared to pay, rather than what you think is the minimum needed to beat the next highest bidder. Hopefully, the full amount of your bid will not be needed and you will get a bargain, but be sure that if someone else beats you, it is because you were unwilling to pay any more than your bid, and not because you simply had not made your bid as high as you might have.
