Can any opening get outdated? Chess getting played since long years with evolutionary advancements. In this process few openings or variations may get outdated. Can it happen so?
The game of chess depends upon outwitting your opponent. Part of the toolbox used by the top players is changing the openings so that their opponents find themselves surprised and unprepared for the new position. This also results in opening variations that are discarded because a flaw has been found.

Openings also go in and out of fashion, for the same reason. The Scotch Opening, for example, first became popular when it was played in a major correspondence chess match between the London and Edinburgh Chess Clubs from 1824-1828, at the recommendation of the Scottish player, John Cochrane.*

Here's a summary of how often it was used in the years that followed, as a percentage of all Double King Pawn games (1.e4 e5) that were played in that period:

Period   Period  Scotch 
Begin    End     Opening %
1824     1900,    7.5% 
1900     1950     3.3% 
1950     1989     5.4%
1990     2000    10.4%


The jump in the last period has been attributed to Garry Kasparov's surprising Anatoly Karpov with it during their match in the 35th World Championship in 1990. In addition, for the 16 years after that, from 1990 through 2005, Garry Kasparov had a score of 17-8-0 with it (17 wins, 8 draws, no losses). This drew attention to the opening again.  It has maintained its popularity in the years since that match.

However, the King's Gambit has not gone through the same increase in popularity:

1824     1900,   16.5% 
1900     1950     9.4% 
1950     1989     5.4%
1990     2000     2.9%


From this data, you might think that the reason the King's Gambit is unpopular is because the results that White achieves with this opening are disappointing.  

But that hypothesis can be disproven: In that last period, 1990-2000, White scored 56% with this opening, with only 18% draws. This is a substantially higher rate of wins than in many other openings.

However, at the highest levels of play (players over 2400 ELO), White scores only 51% with this opening! This is very poor performance, when compared with a 55% win rate in all Double KP openings.  So, because they don't get good enough results with it, it's unpopular at the highest level of play. Only 2.2% of all double KP games involve the King's Gambit at 2400+ ELO.

This suggests that players at lower levels are following fashion set by the highest level players, not the actual results they can achieve in practice at their own level.

*The Scotch Game Explained, Gary Lane, Batsford Chess 2005, p.5