There are still some things that we don't believe or question about it....I think that sometimes a quote it's just a quote that 5 episodes later, especially 3 seasons later, can change....

Yes and no. I think Damon has won and lost her respect before and after that.

-_-

I think the word you should use in this situation is "earn", not "win".
I personally think she respected him even before Stefan told him that. I think the moment that was supposed to show it was an episode later, when Damon told Elena "I can't loose you" and Elena replied in a "you won't", thus respecting his fear of loosing her.
I can't say much about it, because respect isn't a theme in DE's relationship. Respect has to do with moral standards and rationally thinking, and DE mostly do emotions and moral ambiguity. It's not a coincidence that Stefan is the one saying it to Damon.

^ I can't change it now...Sorry.... ;)