In Settlers of Catan, is it possible to avoid "losing a won game?"
10 Points On Your Own Turn = You Win!

If you have 10 or more points at any time during your turn, you win the game outright immediately.

From the University of Catan FAQ (emphasis added):


  Q:    Can a player win the game when it is not her turn? For instance, during another player's turn, the player remembers that she has a victory point card and that card along with other points that she accumulated gives her 10 points. Can she win during another player's turn or does she have to wait her turn to play the victory point card and declare herself the winner?
  
  A:    You can only win during your turn. If somehow you earn enough points to win during another player's turn (such as getting Longest Road because another player broke the longest road, or because you remember your victory point card) you must still wait until your turn. However, you can win at any point during your turn, even before you roll the dice. On the other hand, if another player earns 10 points before your turn, that player will be the winner even though you had 10 points first!




Fear the Boot

So, there's a particular mini-expansion called Fishermen of Catan. You can find the rules online (PDF link). This expansion contains the "Old Shoe." Every time your fisheries produce resources, there's a chance you'll draw the Old Shoe card, which can turn your 10/10 VP into 10/11 VP. Oh noes!

Here's a rules quote (emphasis added):


  D. That Old Shoe
  
  One of the tokens shows an "old shoe" that you might
  accidentally draw while collecting a fish token. If you
  draw the old shoe, you must reveal it immediately! Keep
  the old shoe face up in front of you. As long as the old
  shoe is in your possession, you will need 1 additional
  victory point to win the game! So, you would need
  11 victory points to win the basic Settlers game!
  
  There is good news, however! During your turn after
  rolling the dice, you can give the old shoe away! You can
  give the shoe to any other player who has the same or
  more victory points than you. But, if you alone have the
  most points, you must keep the old shoe for yourself!


So, it looks like the Old Shoe can, in fact, "turn a win into a loss" if this scenario happens:


You get 10 VPs on some other player's turn (per the Longest Road example in the question).
Then another player's roll generates resources for you, and you end up with the Old Shoe.
You can't win on your turn because of your new VP threshold.
Another player goes after you, gets to 10 VP, and wins.


However, if an opponent already has a lot of VP on the board just like you, you can do this on your turn:


(same) You get 10 VPs on some other player's turn (per the Longest Road example in the question).
(same) Then another player's roll generates resources for you, and you end up with the Old Shoe.
You roll the dice, then give the Old Shoe away.
Claim your victory immediately (as above)!


This is yet another case where it's useful to hide your +VP dev cards in your hand until the exact moment you claim the win (sine it makes it easier to dump the Shoe).