The game "broke" for me on every try after a while with the melee soldiers stopping to attack, so I wasn't able to see if there was any bigger changes to the core mechanic as time progressed.
In an economics style game like this it's easy to keep the player wanting to go on, you just need to provide a metric for them to measure their progress by and have them feel like their decision shapes the outcome in more ways than one.
For that I recommend two more ingredients for you to build upon:
1. Rock-paper-scissor balancing.
With a shorter time from spawning to engagement and an additional unit type (fast cavalry?), you can give the player strategic choices to make about which units to spawn and to react to the battle as it goes on. Every unit is strong against one type, and weak against another, just like in "rock paper scissors".
2. Planning intermission
Between eras or battles you can give the player access to a tech tree or unit upgrades, where they can choose the direction they want to improve in, or even plan what units to send into battle next round. This acts as a breather for the player, a save point for progress, and motivations to do another battle to unlock more stuff.