A towel that has stopped taking up water feels like a manufacturing fault, and it very rarely is. Cotton does not lose its ability to absorb. What happens is that something gets deposited on the fibres and sits between the cotton and the water. Almost always it is one of four things, and three of them are reversible in a single wash.
1. Fabric softener
This is the cause in most cases, and it is worth being blunt about it: fabric softener and towels are incompatible. Softener works by coating fibres in a thin layer of waxy, water-repelling compounds. That is what makes a shirt feel smooth. On a towel, whose entire function is to attract and hold water, it is precisely the wrong treatment. The effect accumulates, so a towel does not fail suddenly (it declines over a few months until one day you notice you are pushing water around your arms.
Dryer sheets do the same thing by a different route, depositing the same sort of coating in the tumble dryer. If you use them, they are as much of a problem as liquid softener.
2. Too much detergent
Detergent has to be rinsed out, and a full drum of thick terry towelling is one of the hardest loads for a machine to rinse. Use a full dose on a full load of towels and a fraction of it stays in the pile, where it hardens into a residue that behaves much like softener. Half the recommended dose is enough for towels in almost every machine, and the towels will come out cleaner, not dirtier, because what is left behind is what makes them feel stiff and grey.
3. Hard water
In a hard-water area, calcium and magnesium precipitate out during the wash and deposit on the fibres. Over time this builds a mineral scale in the pile that stiffens the loops and blocks absorption. It also makes detergent less effective, which tempts people into using more, which compounds problem two.
4. The finish on a brand new towel
If the towel is new and has never worked, this is your answer and nothing is wrong. Towels come off the loom with a finish applied during manufacture that leaves the cloth smooth and water-repellent. One wash removes most of it and two or three washes remove the rest. A brand new towel genuinely does not absorb properly, and it is not a defect.
How to strip the build-up
Run the towels through a hot wash) 60C is fine for the ones rated for it (with no detergent at all and about a cup of plain white vinegar in the drum. The acid dissolves both the mineral scale and most of the softener residue. Then run a second hot cycle with nothing in it at all, to rinse the vinegar out. Dry them properly afterwards, ideally with a low tumble finished slightly damp and then hung open.
Do not use vinegar and bleach in the same wash or in consecutive washes without a rinse between them. It is a genuinely dangerous combination.
Most towels come back from this. If yours do not, the pile has probably been worn flat rather than coated, and there is no way to raise a pile that is gone.
Keeping them working
Half a dose of ordinary detergent. No softener, no dryer sheets. Wash at 40C for ordinary use and 60C when something needs sanitising, on the understanding that hot washes shorten a towel’s life. Tumble on low and take them out slightly damp, or line dry and give each towel a hard shake before hanging it) both of those open the loops back up. Above all, hang them open rather than folded, because a folded towel dries only on the outside.