I just had this happen to me as well, but amusingly enough it seemed the AI weren't willing to upgrade their military units either. 150 turns into the game (Epic speed, normal sized Aboria map) the AI that were still around continued to use Warriors with some Javelniers thrown in. Only Barbarian-spawned cities ever had anything else: I saw plenty of archers, a single Chariot, and a few Javelins, but nothing other than warriors and the odd Javelin from the main AI's.
Almost 300 turns in, around 2500BC, I opened the world builder to see what the last remaining AI was doing, and he had a grand total of three units - two workers and a warrior. Despite that, he was researching Engineering just like I was. I immediately declared war and walked my war elephants into his city, ending the +18 relations we had and winning the game.
Not expanding until later in the game is one thing, but the AI this game never even built any metal units like Axemen or Spearmen - Not once! D:
*Edit* New game, and I saw that some of the AI civs that emerge from Barbarian cities would build new cities, still in 1800 - 1300BC years, but not the regular AI that I started with.