Here they fought for 4 Days, ammo is not mentioned once, so it probably was not a problem for them to fight for that long without running out of ammunition:
https://en.wikipedia.org/wiki/Four_Days'_Battle
In this icident brought to my attention by Liq, two frigates fought eachother for 14 hours straight, until the danish frigate ran out of ammunition:
https://en.wikipedia.org/wiki/Peter_Tordenskjold
also not a problem for us, or do you know of anyone who spends 14 hours in battle without docking inbetween?