It depends on the tactical situation. When an army is on the defensive and being pressed it is not possible to risk bringing ammo forward. Artillery batteries would withdraw not only to replenish ammo but also refit the battery for losses and damage incurred.
Reserve batteries would be moved into position. This is why having batteries in reserve is critical. Such was the situation for the Union at Gettysburg who maintained batteries in reserve to go into action when and where needed.
An army on the attack that was directing supporting fire might be able to bring ammunition forward to the guns when not under fire, but even then it was more often that these would retire to be replaced by fresh batteries so they could rest and refit.
For infantry, attacking infantry would always retire when ammo was depleted, and historical records show this almost universally. Defending troops that were being pressed would also retire when ammo was low unless holding an extremely strong position such as Jackson's men on Stony Ridge at 2nd Bull Run (who repulsed an attack throwing rocks!)
Lulls in the battle would also dictate the ability to have ammo brought forward, particularly at dusk, but for our games, these events are outside of the scenario for the most part.
From a historical perspective the most common occurrence would be if low, or out of ammo (infantry or artillery) the unit will disengage the fight and withdraw. The men would be exhausted anyway and would need to be relieved by troops and batteries in reserve.
Tactical doctrine for artillery in the Union army (in the east) would restrict the amount of ammo used so as not to run out. When not pressed, ammunition to the guns would be taken from the rear ammo chest of the caisson first to allow the caisson to be sent to the rear to replenish ammo while ammo from the gun limber was still available.
This tactic was discouraged when under fire as the batteries under heavy fire would redeploy to a safer position and the caisson might not be able to find the re-positioned battery to bring up more ammo.
For tactical battles there really is more than enough ammo for artillery. Union at Gettysburg had four ammo chests per gun, 32 rounds per chest for Napoleons, 50 rounds for rifles.
For a 12-pound Napoleon each chest had 12 solid shot, 12 spherical case, 4 shell and 4 cannister rounds. Rifles had no solid shot, 20 spherical case, 25 shell and 5 cannister.
Total ammo per gun as deployed would be 128 for napoleons, 200 rounds for rifles.
Infantry in a heavy firefight would usually run low on ammo, artillery batteries not so often.
Kim