I find my army is typically the one who's reinforcements are delayed nearly every time. I had 4 armies attacked by 3 armies of the senate. I get 1 army on the map, they get 3. Somehow my initial army survived long enough for the reinforcements to finally arrive and finish off the senate.

I think the number of men involved in the battle and the chances of reinforcements being delayed are related. If all 7 armies were fighting at once, I'd have over 13,000 men killing each other. No way my PC can handle that. Just about every battle I've had with reinforcements that bring the number of men involved to over 5000-6000 has a great chance of the reinforcements being delayed. Perhaps the number of units (and not the individual men in the unit) involved in the battle is the key though. I don't know. I very much imagine I'll never have a battle with 10,000+ men all fighting at once though, reinforcements will be delayed I can almost certainly guarantee.

I also wonder if the attacker's reinforcements are more or less likely to show up than the defender's or whether its random or based on something else entirely.