It happens as a result of the way Civ was designed. In a general Civ game, half of the turns occur between 4000BC and the end around the time players begin industrializing, about 1500AD. Turn-wise, you still have half a game to play after 1500AD!!

Psychologically, you no longer feel like you are making progress because the years per turn gets much lower. The first half of the game covers 5500 years of human history, and the second half only 500. (roughly)

Production times (in turns) for units and improvements is often very high for the more advanced units and improvements...you wait longer for your projects to complete which could make the time more tedious and/or boring.

Your Empire and the empires of your opponents are also getting porgressively larger. It takes much longer clock time to complete a single turn that in the beginning of the game.

SOLUTIONS:
-Play at a more difficult level. Turns cover more years, so there are less turns over all. The decreased amount of time and the higher difficulty may restrict Empire sizes allowing for faster turn resolutions.
It is also common that people get bored around this time because it is the point where you can evaluate your advantage. People get bored because they know they have already won and it is just a matter of developing the world. Play at a level that will make you struggle to the very end.
-Try different strategies during your game. This will depend on how far ahead you are, but set goals for yourself. Like "I am going to concur the Mongols by 1600" or "I will discover Genetic Engineering before 1700." Then devote all of your attention to achieving that goal...build as many units as possible, or maximize your science output, etc. Try different forms of attack or handling diplo relations.
-Try an overall different strategy. Those who get bored the most often around 1500AD tend to be the expansionists. Instead, limit the number of cities you have and figure out how to maximize science and production to get to Alpha Centauri.
-Play on a small map where contact happens much more often.
-Experiment to learn different aspects of the game that you hardly ever use.

In this matter, CIV differs from chess in two important ways:

(a) games can end early by the player essentially claiming victory, rather than by resignation. OK...

(b) Unlike chess (and similar games), there's no easy way to PRACTICE endgames and get separately good at them. This is, however, a correctable problem. We need some CIV website (say, this one, or civ.cx) to collect some interesting late saved game positions, that people can load and play out. The players who contribute these save files can note how well they actually did, as a sort of "par" challenge.

All we need is (1) a place to put these files, and (2) players to remember to save really critical late game positions (say, after 1800) when they come across them, to upload and share with others. Anybody got an exciting fantasy endgame position?

- toby

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Scouse Git[1]