People rarely ask this out loud, which is a shame, because it's the sensible question and the answer is good. Paper carries an association with impermanence: newsprint going yellow, a poster gone brittle at the edges, something in a box in a garage that crumbled when it was moved.
Those things happened for specific reasons, and the reasons are avoidable.
What actually destroys paper
Almost always acid, and usually the paper's own.
Wood pulp contains lignin. Lignin breaks down over time into acidic compounds, and the acid attacks the cellulose fibres around it. That's the yellowing and the brittleness, and it's a chemical process happening inside the material regardless of how carefully it's stored. Newsprint is the extreme case because it's almost entirely pulp.
Remove the lignin and buffer what's left and the mechanism stops. That's what acid-free means, and it's why documents on rag paper from several centuries ago are in better condition than newspapers from the 1970s.
Everything I cut is acid-free mat-board, which is the same material class used for museum framing and archival mounting. Not because it's a nice touch, but because the alternative has a known failure mode and a known timeline.
The adhesive question
A stack of twenty layers is held together by glue, so the glue matters as much as the board.
I use PVA, the same archival adhesive bookbinders have used for repairing and rebinding for a long time. It's pH neutral, it stays slightly flexible rather than going glassy and cracking, and it doesn't yellow or off-gas into the material around it.
What it isn't is forgiving of quantity. Too much and the board warps overnight, which is a piece lost. Too little and the bond fails within a week. The right amount is something I learned by feel over years and still can't express as a volume, which is one of several things about the assembly process that resist description.
Rubber cement, spray adhesive, and most household glues fail one or more of those tests. They're why a lot of older paper work has stains bleeding out from the joins.
Light is the real threat
Assuming decent materials, the thing that will age your piece is light. Ultraviolet in particular, but visible light contributes.
What light does to a work like mine is fade the colour. The board is dyed, and dyes are more vulnerable than the substrate holding them. The structure will be fine long after the colour has shifted.
The mitigations are unglamorous and effective. Don't hang it where direct sun lands on it at any point in the day, which is a stronger constraint than it sounds and worth actually checking across a few hours. Indirect daylight is fine. Artificial light is largely fine, and LED is better than halogen because it emits less UV and much less heat.
If a piece has to go somewhere with real sun exposure, UV-filtering acrylic glazing is the answer. It costs more than glass and weighs less, and for relief work I'd want it kept far enough off the surface that it doesn't flatten the shadows, which are the reason the piece exists.
Humidity, briefly
Paper takes on and gives off moisture, and it changes dimension slightly when it does. A stack of layers moving at slightly different rates is a warp risk.
Ordinary indoor conditions are fine. What to avoid is a bathroom, an unconditioned garage, an exterior wall that gets cold enough to condense, or directly above a radiator. Stable matters more than any particular number, so a room that stays roughly consistent is better than one that swings.
What I don't know
I've been making these for a few years. I can tell you the materials are the ones conservators specify and that the failure modes of the alternatives are well understood, and that's a strong basis for expecting a long life.
What I can't do is show you a piece of mine that's forty years old, because none exists. Anyone in my position telling you with certainty how their work will look in 2070 is guessing with more confidence than the evidence supports. What I've done is choose materials whose behaviour over that span is documented from other uses, and build in a way that doesn't introduce a weakness the materials don't have.
Practical care
Very little, which is most of the point.
Dust with a soft brush or a puff of air rather than a cloth, since a cloth catches on cut edges. Don't clean it with anything wet. Handle it by the edges or the frame, because skin oils on board are permanent. If it needs to be stored, keep it flat and separated from anything that isn't archival, especially cardboard and newsprint.
Then mostly leave it alone. Hang it out of direct sun, in a room you'd be comfortable in yourself, and it will outlast the wall.
If you're deciding where a piece should go, how the light in a room changes what it does is the more interesting half of the same question. And if the materials question came up because you're weighing whether a physical object is worth it at all, this is the argument for the object.
Shawn Kemp makes one-of-a-kind generative artworks fabricated as dimensional layered relief sculptures in Bellingham, Washington, from acid-free mat-board and archival PVA.