Why does my lift-up cabinet door slowly sink back down on its own?

I ran a shop that did kitchen refits for a decade, and this exact complaint came up constantly. It's the strut, almost certainly. Those lift supports are sealed gas cylinders with no adjustment of any kind, so there's no tweak that brings a weak one back. Once the internal charge leaks down, the door starts sagging exactly the way you're describing, slow at first and then all the way shut.

As for why one died and its twin didn't, that's just how seals fail. One unit can have a tiny flaw in the seal from day one and lose pressure over years while the identical one next to it keeps going. Equal use doesn't really factor in. Also think back to wether anything heavy got stored up against that door, or whether stuff inside the cabinet ended up pressing on it. Extra load wears the strut down faster.

Your mounting screw theory is worth ten seconds of checking since you had the door off anyway. Snug up the brackets on both ends and make sure the door sits square. But a geometry problem usally shows up suddenly, after the door gets bumped or a hinge screw strips out. A slow creep over months is the signature of a strut losing charge, not loose hardware. When you buy a replacement, match the force rating printed on the old cylinder body. Too weak and the new one sags just like the old one, too strong and the door snaps up hard when you open it. Easiest move is to pull the old strut and take it with you, or at least measure it extended and note the numbers on the label. And watch the orientation when you install it, rod end pointing down, so the oil inside keeps the seal lubricated. The swap itself is trivial. Usually a clip or a single screw at each end, ten minutes with a screwdriver. No need to touch the door hinges at all.

It sounds like you've got a classic pressure failure, wich is what the other guys are saying. But before you order replacements, you should double check the overall mounting point for the door itself. Sometimes if the cabinet frame has shifted even a millimeter, the door doesn't sit perfectly square even when the strut is fully charged. I had an issue like that last year and the only thing that fixed it was using a small piece of felt shim behind the hinge base to correct the tilt of the whole unit. It seemed like such a tiny thing, but it changed the way the door interacted with the track.

Even if the strut is weak, if the door is angled down slightly, it will take significantly more force to hold it open. Just make sure the top and bottom of the door are level before you decide to swap out the gas cylinder.

I think focusing only on the internal pressure being the problem is too quick. While I agree that the gas can leak, I've seen a couple of cases where the issue isn't necessarily the gas going down, but the mechanism itself binding. If the rod or the housing has dried oil or rust preventing smooth movement, the door will creep down slowly, which looks exactly like a weak strut when it's actually just a mechanical friction problem. Before jumping to replacing the whole unit, maybe check if there is any debris trapped in the pivot points, or if the linkage has shifted off alignment because the door frame is slightly swollen from humidity? It's a cheap check compared to buying parts.

I wonder if the structural integrity of the door hinges themselves coud be contributing to the gradual downward creep, regardless of the strut's operational status. If the hinge mounting screws are not seated optimally within the frame, or if the pins are slightly worn, that could introduce a minor downward leverage on the door panel. This minute, constant strain might be subtly stressing the cylinder housing, even if the internal gas pressure remains perfectly acceptable, causing a faster perceived degradation of performance. It is worth thoroughly inspecting the entire hinge assembly for any signs of deformation or play before ruling out the door supports entirely.

I've seen this happen before when the door isn't sitting perfectly centered on those hinges. Even a tiny bit of weight shifting to one side makes the strut work harder on the other side and stresses the seals. Before you order a replacement cylinder, try checking if the weight is distributed evenly inside the cabinet. My trick is to push the door closed and then pull it back open just a little bit. If it holds that slight angle for a few seconds, it suggests the issue is mechanical wear somewhere else, not the gas totally draining. It's often just about getting the load balanced.