Why does my family SUV develop a stale smell even though there is no single obvious odour source?

Because you have been looking for the wrong shape of thing. The question as most people ask it assumes a culprit — one item, one spill, one surface that is letting the side down — and in a vehicle that carries children every day that assumption is usually false. What you have instead is nine or ten small contributors, each sitting below the level at which anybody would identify it, all adding into the same shared volume of air. A pair of shoes in a second-row footwell is beneath notice. So is the slightly damp corner of a school bag, the carpet underneath the mats, the sticky ring in a cup holder, the half-finished bottle that rolled under a seat in March, the umbrella that went in wet on Tuesday, the channel where a folded third row meets the floor, the seat-back pockets nobody empties, and the crumbs worked into a seat gap. Individually each one is nothing, and if you held any of them up to your face you would say so honestly. Together, in a sealed cabin overnight, they make a background that is unmistakably present and impossible to describe — and the reason you cannot describe it is that it does not belong to a category. It is a sum. Your nose is good at recognising damp, or sour, or sweet; it has no word for one ninth of each. That changes the method completely, and this is the useful part of the page. Searching is the correct approach when there is something to find. Here it produces an hour of sniffing, no answer, and the quiet conclusion that the vehicle must need something stronger. The approach that fits the mechanism is an inventory: list everything in the vehicle capable of contributing anything, then deal with the whole list without arguing about whether any individual item deserves it. It is less satisfying than catching a culprit — I will not pretend otherwise, and most people find the first run of it faintly ridiculous — but it is the version that moves the morning reading. One thing worth saying before we start. Fragrance will not remove this. A car perfume adds a scent to the cabin air and has no mechanism for taking one out, so putting something strong into a cabin already carrying nine small contributions gives you ten things at once rather than one. Intensity is a shared comfort decision, best judged by a passenger climbing into the back row for the first time rather than by the driver who has been sitting in it all term. And nothing on this page is a claim about driving, alertness or road safety.