The room was never the prize
Watch what she actually does in the sixty seconds after you open the door. Most cats walk a circuit: along the skirting, around the bed or desk, a sniff at anything that has moved, a cheek rub on a chair leg, and then they are at the door again, asking out. That is a completed patrol, not a changed mind. She wanted to verify that a piece of her territory still smelled right and held no surprises, and once the inspection is done the room has nothing more to offer until the next round of changes accumulates.
Closed doors offend a cat's sense of control
Cats organise their lives around free movement through a known map, and a closed door is an interruption in that map they cannot fix themselves. The frustration is about the barrier, not the destination, which is why the same cat will campaign at a cupboard, a spare room she never sleeps in, or a bathroom she intends to leave within the minute. Being able to come and go is itself the resource. This is also why door-campaigning often intensifies at night, when several doors close at once and her whole patrol route shrinks without warning.
Smell is the news she is checking for
Your cat reads the house largely by scent. While she has been shut out, smells have changed in that room: laundry moved, a visitor's bag arrived, yesterday's cheek marks faded. Her circuit refreshes her own scent from glands in her cheeks and paws and updates her picture of what belongs there. A room that has been redecorated, deep-cleaned or filled with new furniture will earn longer and more frequent inspections, and a new pet's smell behind a door can turn polite requests into urgent shouting, because the news behind that door is genuinely significant to her.
Workable compromises for a household that needs doors shut
You cannot live with every door open, so reduce the value of the closed ones. Where privacy allows, leave doors ajar or fit a cat flap or a door strap that holds a cat-width gap to the rooms she patrols most. For rooms that must stay shut, let her do one supervised circuit at predictable times, such as when you get dressed or before bed, so the inspection happens on a schedule she can learn. Never make a game of opening and closing at her demand through the night, because a cat who learns that persistent calling at 3 a.m. works will, reasonably, keep doing it.
When in-and-out restlessness is a health flag instead
Ordinary door campaigns are relaxed, unhurried and fitted around an otherwise settled day. Restlessness looks different: pacing from room to room without settling anywhere, calling in a lower or louder voice than usual, repeated trips to the litter tray, or an older cat who seems disoriented by doors she has known for years. Those patterns, especially starting suddenly or paired with changes in appetite, thirst or sleep, warrant a vet visit, since pain, urinary discomfort and age-related confusion can all present first as a cat who cannot settle in any room you open for her.
Sharing door duty across the household
In many homes one person becomes the designated door-opener simply by answering first, and the miaows all aim at them. KinsLe's Care Teams lets you spread the surrounding rounds, the feeding, litter checks and evening room circuits, across the household with named owners and timestamps for finished tasks, so answering your cat's patrol requests stops resting on whoever happens to be nearest the door.