Cities don't last forever. Most of the ancient world's greatest cities are now just ruins or entirely non existent. I think it would make for an interesting game mechanic if cities, outposts, and administrative centers had limited lifetimes after which they would fall into ruin.

The minor civilizations that pop up randomly already do this. I'm not sure what the mechanisms are that determine how long they stick around, but it at least shows that the capability is already there. My idea is that major empire's cities would start with a limited amount of turns and outposts/administrative centers would have a quarter as much as full cities. After the time runs out, the city falls into ruins and the population and territory are lost. The player can either reclaim the ruins and rebuild or leave them for another empire to pave over.

I figure that about 100 turns would be the maximum amount of time a city could last on normal speed which should translate to about 2 eras. However, the time it takes to fall apart would be doubled if stability is low and the population is stressed, and quadrupled if the city is in rebellion. Perhaps you may be able to reset the timer on outposts by attaching them to cities and also city timers could be reset by absorbing them into another city. Of course these options come with a stability penalty so it could just speed up the ruining of both cities.

The reason I like this idea is because I was kinda put off by the fact that my medieval empires could span an entire continent by 500 BC. Real world empires don't encompass the entire area of every tribe and civilization that came before them. You take the land that is good, keep it for as long as it's useful, and then move on to greener pastures. I think this idea works really well with the changing of factions system this game has. With this idea, an empire could slowly move across the world without having to manage and protect entire continents as it goes.

There are settlements inhabited continuously since bronze age. There's a lot of settlements inhabited since antiquity. Great majority of medieval cities is still inhabited as well. Your entire point is invalid. 

Well the point is for the cities to last multiple eras and possibly even longer with some effort, so you might be able to keep a city from ancient to contemporary age but likely not all of them. True there are several examples of cities that have lasted since medieval times and earlier, but I'm sure there are plenty of examples of ones that didn't, some of which we may never even know about because they are just gone.

Anyway, the point of my idea was not to be completely realistic, but to introduce some limitations to the amount of area an empire can control. Currently, you can slap down cities and outposts forever, so long as you have enough influence, and eventually you could gobble up the entire world and steamroll the other players. All I wanted was to slow down that process and make it more difficult to spiral out of control with territory. It didn't make sense to me that global domination could be achieved so easily by the renaissance period. Also, Amplitude thought it made sense for the minor factions to have limited lifespans so why not major faction cities as well?

I do like this idea.

Nevertheless, I think it is important to have some mechanism to stop the fall of a given city, if I envest enough resources in it (mainly gold or influence). Maybe every half an era you should be required to pay a maintanence cost to reset the ticker. Also, if the city falls you should have the option to save it, but at a higher cost, and this time the new (or saved) city would be renamed after your current culture.

I love that idea too. In that way you could either keep your ancient cities or reclaim them for a price but you get the new era artwork for the city center and a new name. I would try to put a cooldown on it as well if you let the city expire so that you risk allowing another faction to take control during the time it takes to rebuild.

I was also thinking that this could be a way to make the nomadic era a fully fledged era. Instead of outposts for future cities you lay down nomad camps that have a very short lifespan but still allow you to gather food quickly to increase your population and even do some research.

I think encoding a hard limit on how cities last is a bad idea, but I have thought this before.

What would naturally make sense is that ancient cities, somehow, fail to scale into later eras, or may fail to take advantage of later era resources. Players can stick with their city and keep it updated at cost, but making a new city from scratch will keep you up to date. To me, the best benefit of this is that it would make losing cities hurt less - I think it would be nice to see borders be able to change more drastically without a player being curbed due to losing a heavily invested city. In extreme cases, a player might totally abandon a continent filled with enemies in order to focus on cities in a more isolated location.

Maybe districts need to be rebuilt in order to take advantage of changing infrastructure? 

Right. Enforcing a hard turn limit on cities is a pretty poor way to go about it. Like aguaacrobata said, there should be a way to invest resources into a city to prevent its demise. There's already a tech that give new cities all the infrastructure from previous eras which is actually really nice and a huge incentive to keep expanding in the later game. And if the player had to potentially choose between maintaining the new powerful cities with all the infrastructure already built in or trying to keep and update the old cities, it could lead to some dynamic and interesting border shifting.

The rebuilding of districts to keep them updated idea is also a simple but effective solution. However, it's not enough on its own to potentially encourage me to abandon a city. But, if the population from a dying city instantly migrated to a nearby city of the same empire that would be a huge incentive to let old inefficient cities go.