The timer in the battles are great for a challenge – but having to replay a battle for running out of time or just losing the battle when you just need 1 more turn can take a little from the players experience for me and likely also other people.
I would either allow players to select from the beginning of a campaign if they want strict or relaxed deadlines. Possibly you could also get a chance when times runs out to get an extended time frame at the cost of prestige/money