This is absolutely off-topic but it's nothing unusual for soldiers to be under extreme pressure for even days of constant combat or long hours before they can really take a proper rest (when adrenaline goes down and body can really rest, not just catch a breath). Same in older times for example during sieges where fights could be going for long hours before both sides had to call it a day and rest. Hell, a proper big scale battles between two armies could last for few hours. Surveillance from cops many times required a 12h without sleep activity.
There is nothing unrealistic in fight after fight without rest. Actually it's quite common during a war or extreme situations (and those are extreme situations during campaign). And since we don't have adventurers chasing for cults and dragons in real life- this is closest comparison you can get when it comes to that.
I don't think it breaks immersion, I actually think it increases it.
But that is off-topic and very table-dependent so let's drop it.