Limiting the lifetime of the gladiators hurts at first, but is inevitable to establish a healthy economy.
But do not worry, we got you covered. Gladiators do not get hurt or die in regular fights. Each gladiator has 2000 Life points to spend.
1 fight takes away 1-3 life points on the outcome: 3 points for a loss, 2 points for a win and just 1 point if that was a flawless victory (loosing only very little stamina).
1 school visit takes away 5 life points.
If you choose to take the schooling route, after around 100 visits your gladiator is top notch trained at a master gladiator level. That would take away around 1/4 of his life points.
Let's check playtime:
Let us assume you need to wait 1 minute for matchmaking, 1 minute for class selection and 4 minutes for the execution of a fight, that would add up to 6 minutes for a fight cycle. The lifetime system will give the player around 650-850 fights in a realistic scenario - that are net 65-85 hours spent in matches and matchmaking. Plus you would spend a significant amount of time for research and other things. So the casual gamer investing around 2 hours per weekday would have 2 months playtime having only one gladiator.
So, do not worry, your gladiator is gonna last for quite some time and if you make it up to a master in any skill, you get that school for free that will outlive the character and be there forever.