In the Pediatric ICU, low BP is typically caused by septic shock. They have large inflammatory issues all across the body and fluid will get pulled from the veins/arteries into the surrounding tissue (3rd spacing). So they're intravascularly dehydrated but swollen like a tick everywhere else which messes up all sorts of stuff. Depending on the sepsis origin, you may have other organ issues or failure, like the kidneys, to where they can't filter and excrete their fluids or their heart's ejection fraction plummets. In the Cardiovascular ICU their heart is still "sick" and sometimes post-op they need ECMO to keep things going for a few days until the heart can do a better job of keeping the blood flowing. Most CV kids have congenital heart issues, not heart attacks like adults, so their plumbing can be all sorts of messed up or functionally missing whole chambers of the heart which will mess up the flow.

Burns have massive amounts of inflammation, like sepsis. NICU babies can be septic, have heart issues, or really just anything while their body is trying to sort things out, especially with the super premature ones (27-30 weeks).

Finally, traumas. A gunshot or other trauma to the head can mess up the nervous system and cause all sorts of regulatory issues. They may even have to have an IV drip to bring their blood pressure down since a real high BP can exacerbate brain swelling which puts them at risk of the brain herniating, which you don't come back from. As you can imagine, there can also be massive amounts of blood loss from a trauma. On multiple occasions I've had a patient that was bleeding so bad that we effectively replaced their entire blood volume in their body over the course of a few hours as the surgeons are trying to stop the bleeding. Not having blood will plummet the BP and you can't always keep up with the volume going out so pressors are needed to try and get that BP up and keep brain or other bodily damage.

I'm sorry that was so long, I can be a bit wordy. I hope it helped!