Depends on many factors:
Glue used for binding: There are very durable and good glues around, for instance PolyUrethane-based glues. The best technology - and the oldest - is stitching, literally sewing the signatures together. It’s not usually an option for paperbacks though there are exceptions.
Paper: There are many hundreds of different qualities of paper, roughly distinguishable in two groups: papers containing wood fibres, and papers not containing wood fibres. The difference is not in the basic ingredients, it’s still a pulp made from wood, but in the processing. Papers containing wood are cheaper, as not all of the raw material is processed so that only the basic cellulose remains. The problem is, that the unprocessed lignine and other wood residue leads to a degeneration of the paper, in the short term visible by the paper yellowing in sunlight, in the long term compromising the bonds between the paper fibres. The paper becomes brittle and slowly disintegrates. There have been advances in paper technology, even the cheapest paper will nowadays take a very long time to really suffer, but the process is still at work.
Cellulose-only paper is much mor stable, as there is just the cellulose-molecules and the glue to bind them together to be taken care of. Since the nineties the glues used in papers have become acid-free (meaning they will not degrade into acidic components over time that might hurt the cellulose) and thus the estimated life-span of a simple paper is now safely in the hundred year range again.
Storage: Cool and dry, away from wood-lice, fungi, what you will. As cellulose can be broken down to the basic sugars it’s made of (with effort), some species like to eat paper.
So taking into account what I know of American (or English) paperbacks I’d estimate that a cheap paperback would probably last 40 years, a higher quality book might last a hundred and could then still be repaired by a professional bookbinder (if that profession is still known then).
