Do you have specific time period/event in mind or is it open ended? It's been rare that there is entirely unceasing pitched combat lasting days on end, even counting sieges. There would have to be a significant force disparity for this to occur, which generally means that full a blown attack wouldn't last more than a few hours. Combat is tiring and even at Thermopylae both sides took breaks at night.
Current US Army doctrine is in Field Manual 3-21-31, Appendix A, includes recommendation for unit rotation. This is part of the importance of having units in reserve.
This is mostly in response to users u/MarkIsNotAShark and u/hobblingcontractor, but because it also answers the OP question I decided to answer directly rather than in a reply.
Obviously no one can speak to the experience of all soldiers in all of history, but at the very least in WWI (and I’m going to specifically talk about Verdun), they didn’t really sleep not because they were “on call” 24/7, but because the physical circumstances of just lying in cover for extended periods was so mentally and physically exhausting it was just impossible.
I’m going to quote from Alistair Horne’s The Price of Glory which I have heard from other posts may be a bit dated in its analysis of Verdun, but he consistently quotes what appear to be great sources. If anyone else with experience on Verdun can comment or correct me I’d appreciate it!
As u/MarkIsNotAShark noted, in Verdun specifically the French were forced to rotate troops from all over to the front, meaning most every troop who survived the war spent some time at Verdun but it was a short time, while the opposite is true for the Germans: less German soldiers participated at Verdun (relative in proportion to the army as a whole), but those who did stayed there much longer, if not for the entire duration of the battle. I can’t speak to other battles that fit this multi-day battle/campaign format such as the Somme, but at Verdun at least, life was so hellish on the front soldiers couldn’t sleep and weren’t even expected to.
There was so much shelling in such a small concentration of land (once the initial German advance petered out by February 28, both sides rarely had less than 200 guns each in this sector that was only about 10 miles long) that trenches effectively ceased to exist. Under such bombardment, any intricate and deep trenches eventually became shallow ditches of mud.
“One of the first things that struck troops fresh to the Verdun battlefield was the fearful stench of putrefaction: “so disgusting that it almost gives a certain charm to the odour of gas shells” ...at Verdun an attempt at burial not infrequently resulted in two more corpses to dispose of. It was safer to wrap the dead up in a canvas and simply roll them over the parapet into the largest shell hole in the vicinity...to one eye-witness it seemed as if it [a gully on the right bank of the Meuse called La ravine de la Mort] were filled with the dismembered limbs that no one could or would bury.
These descriptions continue for some time but Alistair Horne does eventually speak exactly to this question about sleep.
“All day long the enemy guns worked at levelling the holes laboriously scraped out the previous night. At night, no question of sleep for the men worn out by the day’s shelling (it was not unknown for men in the line to go without sleep for eleven days)...
[my note, I take this to mean that soldiers were not given time explicitly slated for sleep for 11 days, as far as I’m aware human exhaustion kills you in about 7]
...By dawn the trench would probably be little more than eighteen inches deep, but it had to be occupied all day, while the enemy gunners resumed their work of levelling.
I’ll close with part of a quote Horne attributes to Paul Dubrulle, a “thirty-four year old French jesuit serving as an infantry sergeant at Verdun.”
“When one heard the whistle in the distance, one’s whole body contracted to resist the too excessively potent vibrations of the explosion, and at each repetition it was a new attack, a new fatigue...Under this regime, the most solid nerves cannot resist for long...where fever burns the body and where the nerves, exhausted, become incapable of reacting...finally one abandons one’s self to it, one has no longer even the strength to cover oneself with one’s pack as protection against splinters...To die from a bullet seems to be nothing…”
Again, I ask anyone more familiar with WWI or Verdun in particular to please correct me, but as far as I am aware, at Verdun at least fighting could be and was so hellish, fierce, and all-encompassing that such creature concerns as sleep and burial were not even considered, and would be left to the individual soldier to decide how to deal with them under such bombardment.
edit completely forgot my citation sorry!
Horne, Alistair. The Price of Glory, Macmillan publishers, Great Britain, 1962 (175-177)
Horne quotes Dubrulle from: Dubrulle, Paul. Mon Regiment, Paris, 1917 (as a side note, Dubrulle survived Verdun, but died the next year in the Nivelle Offensive)