When did the other person bid? If you click on the bid history it will give you the time "to the second" when the auction ended and when the winner placed their bid.
Also, which screen were you watching? If you watch the auction screen if shows bids as they pile up but if you watch just the "Confirm your Bid" screen it doesn't.
That means if you want the "Confirm" screen open to enter your snipe, you need to also follow the auction in a separate window.
Better yet, when you are really serious about getting the item, decide what is your MAX (the highest you can possibly go, not the low price you hope for) and enter your snipe in the last few seconds of the auction before someone else has time to overtake it. If your bid is highest, you win every time.