Context:
DNA from shed skin cells, or touch DNA is actually quite durable.
It can be degraded by a number of things, though. These include heat, humidity and bacteria.
If you made contact with clothing and then set that item aside, lets say in a cool closet in a basement, that DNA could easily last for years.
In a hot, humid environment it could last from a few hours to a few days, depending on how quickly bacteria levels increase.
DNA can survive the washing machine, although that is more applicable to DNA from blood or semen. The problem with touch DNA is it simply doesnt have the quantity of cells that DNA from bodily fluids can deposit.